A provider I know was in a session with a guy who started to have a seizure.  She called 911 and stayed with him until the paramedics arrived.  I don't believe they asked any questions about what the relationships were. They are simply there to save a life.  So the answer is, do what this woman did.  
I later met them both at a M&G and she introduced him as "Stroke Guy."  It wasn't actually a stroke but she thought it was funny.  Then again, she has more balls than many guys I know.

A medical emergency has not happened while with someone of the Hobby.

I would call 911, stay and take care of whatever needs to be taken care of-including whatever is going on with him, I would not give my name- or would give a fake name and pretend to be family if had to, and likely I would go to the hospital if he is single to make sure he is recovering (depends on how well I know him).

There is absolutely no reason to not call 911 and stay until they arrive. Anything could happen during that time and it is one shit of a human being to walk away when something is going wrong.  

Saving a life versus just leaving because you are afraid of any highly unlikely repercussions.

Just as long as she left with me a smile on my face, I'm good.  Beats a lot of other ways to depart this world.

This did not happen to me, but... I had an embarrassing experience

One time, about 4 years ago, I saw a provider at her apartment. I have a hairy body and that must of been a turn off to her. She asked me to shave my publc hair before we would play. She gave me this cheap disposable razor. I was like, "Seriously?" I jumped in the shower to try to wet my hair. I started to shave and as I was trying to clear the hair that was clumped in the blade, I knicked the top of my thumb. It began to bleed like crazy. I screamed for her to help. She tried to apply pressure with paper towel and put a band-aid on it. After a few minutes, it still wasn't slowing down. I was a little bit scared. She actually suggested that we continue with our session! I really was not in the mood with my thumb bleeding. She offered to drive me to the hospital, but I had to get back home ( lived with parents at the time and they thought I was working). I couldn't take a chance sitting in an ER for hours and having to figure out an explanation to my parents how I ended up there (no where near my job). Eventually the bleeding slowed down, but I could not enjoy the pleasure the provider tried to give me. I remember stopping at the pharmacy next to the train station and picking up a box of band-aids for the ride home. Fortunately, I made it home with no complications. Although trying to unzip my pants to pee in the men's room in the train station was brutal, lol. Eventually the cut healed on its own without requiring stitches.  

Lesson: never shave your pubic hair ( unless with an electric trimmer) for a woman, even if sex is imminent.

not a heart attack

But I did have a strenuous encounter with a lady one morning. I had major surgery planned about a month later and had to get some tests done. So on my way home I stopped by for the tests......seems my heart was beating rapidly and I was in afib.  The nurse and doctor kept asking me if I'd done anything strenuous that morning. I wish said said the truth just to see the reaction. LOL

so he survives? Lol

None of anybody's beeswax who we are or why we're together.

Call 911
Call the front desk so they know EMS is on the way & to direct them to the correct room.
Unlock the door, so EMS can get in
Do first aid to the best of your knowledge & ability.    
EMS arrives Grab your clothes & run into the bathroom.  
Get dressed & leave.