...just recently had 2 hr appt w local provider..first time meeting...small talk,etc/left donation...got busy...multiple covers...last go round was amazing...vocal orgasms from her-no complaints...till we discovered that we were now 45 mins over...she went crazy-saying that i was a user/ripping her off/asshole/wont see me again/etc....i was shocked...i'm not a clock watcher...i said if time was so important...you should have said something after orgasm 2 of 4 occurred!!...so-as a client,am i supposed to be the time keeper?...offered "a tip" to cover overtime...became big bummer after amazing sexual experience....ladies,am i wrong here?...if its hot,why stop...

I would think the lady is the one who would be the one to keep that in mind, if we kept going I would just assume she really liked me and kept it going Ofc but then again as a gentlemen you do need to be considerate of her time I guess it’s different opinions with this but I’ll say it’s on her

If I'm enjoying myself and time goes over that's on ME. Is it nice that a gentleman recognizes that we went over and tips...of course.  
I wouldn't over think it.

...and aware otherwise you turn HER experience into a big bummer, ie, she has to go through the hassle of telling you to leave.

but that is minor compared to what you describe as her reaction.  

Even if there's no clock/watch visible, you have some idea of time progressing.  In that situation, if I think we might be getting close to the end of the agreed time, I'll say something like, "Do you know how we're doing on time?"  She can then check the time, or more often than not she'll tell me not to worry about it.  

I would have been so grateful to get off 4 times!! Lol
This lady was highly unprofessional to say the least.  
I get that sometimes it's just great energy flowing that makes the time fly by but I think it's on the lady to keep track of time. I also believe the gentleman should be aware of his own schedule/time but at the same time, why not continue to enjoy yourself if the lady is having fun. Really nice of you to offer a tip. Sorry but this chic sounds BSC.  GPS maybe?
I can only imagine how uncomfortable that must have been for you ☹
XOXO  
TL

So yes we should be in control of the time. If she diddn't manage her time well then reacting like that isn't the most professional way to go about it in my opinion. I wouldn't have reacted like that if it were me and I also generally won't go 45 min over either. (no one tries it anyway)  

I’ve been at this so long I kind know when times up.If she’s a professional she should be aware of the time without you knowing about it. And you as a respectful should do likewise.  

.... I do not condone her reaction. The question was directed at who is responsible not who handled the situation well.

Unless they're trying to get more $$ out of you/playing games.

But the OP seems to think he has no responsibility to keep track of time.  

....appointment. That is such a rush for me. With a two hour, not so much. But, sometimes the chemistry is so great that time can get away from anyone.  
I do try to be conscious of the time. But, my ladies do let me know.  

I have music that keeps me on point timewise.

Two hours, etc.  
Furthermore, even though I can't readily see them  
{as I'm very blind without accouterments, }
my Clients can certainly monitor them.

You could or should have been more considerate of her/your time. And I find it hard to believe that when it came close to the two hours mark that you didn't notice the time or if you were aware of it. You're talking 45 minutes here. You place it on her and you  wanted her to mention the time to you. i don't think you were ever going to mention the time. But there is a "part" of this where she is to blame, but it's mostly on you.
Now if it's outcall, then it would have been on her to monitor the clock. She could leave when the time is near or over but part of you could say, clearing your voice,"I think it's about time". Then it'll be her choice.
Now her going crazy is a bit though....Just my 2 cents

To overshoot by 45 minutes, she should have had some presence of mind as to where the time was. I've never overshot.... for exactly this reason. I'm always thinking that if I book 60, but ended up at 90.... additional compensation would be expected. I have been asked to stay, but that's on them. And it was just conversation and cuddling...for the most part. I think if she expected to be compensated for each minute, that should have been made aware at the approaching end of initial appointment. Now....if you were just continuing to get your groove on as and beyond that time came....compensation should have been delivered.

I would agree it is a shared responsibility.

What's it been? A whole 2-3 days since we discussed this?

Yes, but nobody has been called stupid or an asshat yet. Hahahahaha

Self-esteem boost by bragging about getting a girl off 4 times?

I know without a clock when the time is up. So, for this gal to go bsc is unnecessary. If her goal was to get more money; she could have simply stated her facts.  
Example...I had a gent who asked me to rent a room so we could get together this week. The very next day, he canceled.  The room was nonrefundable and in a city where the hobby is dry. So, I said I will kindly ask you to compensate me for the room. He agreed and nobody gets the shit end.

If we are more than halfway into the booked session I say something to the gal and leave it up to her to timekeep the 2nd half or attempt round 2.  If no 2nd round is in the cards then so be it.  If she wants to try fir 2 its on her.  After round 2,  (if overtime, I will usually tip for her kindly finishing me off)  if she ends it because times up and I am not done, then oh well, thats on me.  Felt good anyway.  I try to be considerate.  I usually rebook with the former rather than the latter though.  I never assume extra time will be available and don't expect it, but I do appreciate heads up warnings rather than hustle and rush "get out" attitudes.  
A few years back I had a gal tell me to take my watch off one time on an hour appt because she wanted me to "feel unrushed".  There was no clock in the room.  After round 3 I went to the restroom looked at the time and realized 2.5 hours had passed.  I had felt time passing and mentioned it to her after round 2 but she had hushed me and went down again.  After retuening from the bathroom when I told her 2 and a half hours had passed she freaked and basically kicked me out of the door half dressed.  Her wonderful "unrushed" session became a sour ending through her own "unrushed" fault even though I tried to keep her cognizant.  Ah well, can't help BSC.

Of course everyone is ultimately responsible for their  own actions, so as gentlemen we want to aquit ourselves favorably. But it is easy to guess that she is a militant third wave feminist liberal progressive Democrat. Because the key to their personality is the belief that they should be free of all consequences of their actions and it should be someone else's responsibility and cost.

It's the subs job to watch the time while the client and the provider are fucking!

Is that the session went over because the lady was so "into" him.  Going over is a business decision on her part based in several factors, including but not limited to, her schedule, her inviting you to repeat, whether she thinks or knows you are a tipper, whether you have behaved as a gentleman, etc.  it's common sense that if her schedule is tight, how much she's enjoying your company has no bearing on whether she ends the session on time or allows it to go over.  

"Doesn't matter how hot you may think it is. It's still work."

Well you started off with good points but your ending makes you look calloused and sarcastic.
Why is he just trying to get all the free time he can get.  How do you know this.  It’s still work!  Nice approach to the job!

about a dozen new reviews a day where guys say something like that.  I have a hobby friend that kept telling me that, and then after about ten sessions with this lady, all of which went overtime, she just stopped taking his appointments, saying it was because he was not respecting the schedule.  So in many instances, rather than get into a dramatic scene about over-time with the customer, they just decide one day that enough is enough.