This probably isn't what you want to hear, but AMP hours are usually scheduled like HS or college class hours.  
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Classes are scheduled at 9 AM, 10 AM, ... 2 PM, 3 PM ...  
To allow travel time between classes (or to allow gents to come and go without bumping into each other), ACTUAL class hours are more like 50 minute hours and class times start at 5-after and end at 5-before the hour.  
9 AM class = 9:05 to 9:55  
10 AM class = 10:05 to 10:55  
(At some places, the class hour is N:00 to N:50 instead of N:05 to N:55 but still a 50 minute hour.)
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I don't think anyone has ever successfully sued a school for only providing 5/6 of the nominal class time. I.e., if a typical college schedule is 40 hours per week for 16 weeks, that's around 12 class "hours" of lecture and 28 hours of reading, homework, and prep time per week and that works out to 12 hours x 16 weeks = an expectation of 192 class "contact hours" (mostly lecture but some class time for quizzes and exams).  
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If you're paying $40,000 per year (2 semesters) for tuition (for a "typical" course load) that's  
($20,000 per semester) / (192 class hours per semester) = $104 per class hour.
If you're only getting 50 minute hours, you are being overcharged by $17 per hour.  
Rather than file a lawsuit, assume that the extra $17 per hour goes to pay for the library, gym, and other amenities (fresh towels, clean sheets, ...).  
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Oh ... back to the AMPs. For simplicity, they try to schedule on the hour: 9, 10, 11, 12, 1, 2 ...
To keep on schedule, each "hour" is a short hour of around 50 minutes or so.  
When the schedule is thrown off enough, the AMPs WILL schedule at a non-N:00 time and tell you to arrive at N:15 or N:30 or whatever but it is still likely to be a "short" hour unless going over gets them back to the N:00 times. I.e., you're told to arrive and ring the bell at 7:40; "start" at 7:45; don't get the knock on the door until 8:50 or 8:55. FULL HOUR!
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The AAMPs (apartment AMPs) are more flexible and the hostesses are more capable of providing a full 60 minute hour.  
The agencies you mention might be strict "50 minute hour" operations but you can ask them if you get a full hour or a 50 minute hour so you'll know ahead of time. But you mention "mamasan" which is more like an AMP.

If you start at 2pm and the next guy is coming in at 3pm, you don't get to keep ducking until 3pm. Girl still needs to take you to shower, she needs to clean herself and the room, both of you need to get dressed. That's your 10 minutes. Blame the  massage parlors for not scheduling buffer time.

And yes your time starts when you walk in the door. Why wouldn't it? If the girl is late getting to the room then yeah you should get make up time, but you're paying for the 1hr of time not 1hr of sex.

Or perhaps you would rather the girl show up to your 2pm disheveled with cum on her from her 1pm because she didn't have time to clean up?

If you want a full unrushed hour, you would be better off meeting with indies. They would be less likely to schedule back to back without buffer time. That being said, you should be respectful to the ladies time because if you take 1:15hr, then you're essentially getting time for free from the girl. Make sure she is ok with it.

Is the second time inclusive?

I feel like the higher end girls arent really clock watchers, and they tend to only see  1 or 2 a week. If you go massage parlors or fast houses, i would assume they want you in and out asap

For my Kinky GFE encounters, I operate based on an honor system where the suitor who is visiting me is in control of when our encounter ends. In some instances, I might be tied up or blindfolded.. Therefore I'm not at all concerned with looking at a clock and couldn't if I wanted to. That's one of many reasons why I have a two hour Kinky GFE / PSE minimum. I'm blessed to have mostly met caring and respectful clients who want to stay on my good side so they opt to leave a few minutes or more before the session ends.

 
Now for a shorter session, such as one that's an hour long, there's usually a mutual understanding about what all makes sense within that tighter time frame. As the client, you know your body and your needs. What's the point of reserving a date that's too short for what you actually want to do? If booking a 1.5 hour appointment is what is most appropriate, just do that. The pace will be more easeful which allows the companion you're seeing to be more relaxed and able to fully focus on fulfilling your desires.

 
With independent companions, if it is clear you want to jam 1.5 or 2 hours worth of activities into a one hour date, that's a quick way to get yourself fired, blocked, and placed on someone's DNS list. So it's actually quite funny to hear that at agencies, a manager will aggressively pound on the door to stop a client from overstaying.

Clock violation

I did my first AMP in the late 70’s at a place on Park Row downtown so I’ve got some history. Forget about 1:00, 2:00, etc. These AMP’s while running a business are like a restaurant. You tip the host/hostess and you get better treatment. My friends $20 smear in NYC at the AMP goes a long way. I have a type I prefer and activities I like to partake in. I’ll get hit up by the AMP if something new is coming in to my liking. Sorry guys if you’re the one behind the curtain waiting on be but I’ve only once in last 10 years got push back about being overtime and I explained it as the providers issue. In any business proposition if they set the price I set the terms. Happy humping brothers

You used the term "mamasan" so I am assuming your are referring to AMP visits. I also have to ask, are you sure you are coming on time for your scheduled visits? Because if you come 15 minutes late and paid for an hour then you need to work out the time before you hand anybody any money. Anytime, my appointment starts late I ask ahead of time if I will get my full hour. A guy who comes late with a girl who has back to back appointments fucks things up for everybody.  

Time is very important and the clock automatically starts at your scheduled time. If for whatever reason you get in late, discuss if you will get your full time before you put any money in her hands. I had an appointment with a high end provider for an one hour appointment. She gave me the room number 10 minutes past the scheduled hour and it took me another 5 minutes to wait for the elevator and for her to open up the door. The first question I asked her was if I would get my full hour because she gave me the room number late. She said no because she had another client at the top of the hour. I walked out because this was not fair to me.  

BTW, providers giving out the location information and room numbers late should be a whole post.