I usually use Asian Mystique and sometimes the girl is surprised if you initiate Round 3. Maybe they aren't used to 3, as BMJ says, but I certainly am in a 2-hour booking.
For example, my second pop with Yuko was all over her breasts, so she went to the shower to wash and came back with her panties already on, by which time I was ready again. With 30 minutes still on the clock, I simply took charge, went down on her through her panties, and pretty soon had her pert bottom up and DS for a third.
It's your money and your time. If you don't initiate, naturally the girl will think her work is done. Just get stuck in and fill your boots up!