It isn't a straightforward situation.
In parlours I have always paid afterwards, however with escorts when no one else is around I always offer the money up front. However in my experience the better punts are from ones who don't bother counting the money.
With Amy who I've seen maybe fifty times I simply leave it on the table, and not once has she even touched it in my presence - even on the first occasion. Another English girl called Tamara I saw half a dozen times in Covent Garden was also exactly like this.
Nicoletta also didn't use to touch the money, and I was once going up the stairs out of her premises when she called me back at exactly the same time as I remembered I hadn't paid! This was a long time ago and she still didn't touch the money even after that. However maybe the last four times I've seen her she has started counting the money and putting it away first. Now I don't mind as her service hasn't changed and remains absolutely top notch, but obviously it is surprising especially as she knows me so well. In my review of her that's what I meant when I said she seems to have become a more professional businesswoman as she has got older. Maybe she has been ripped off in recent years?
Had a couple of EE girls, Karolina in 2011 and Karina in 2007, the latter being a total nympho, who firmly refused my offer of the money up front. I'd already cum twice with Karina when she wanted me to stay over time without any extras charge and try to cum for a third time. I hadn't paid her anything at this point!
The great Carla of Sheffield who I used to do overnights with also would never touch the money beforehand. She always said, 'I haven't done anything to earn it yet' which summed up her fabulous attitude.
The bottom line is with an escort I would always offer the money first, especially if I hadn't seen her before. It gets it out of the way, shows you aren't going to do a runner and is therefore more likely to make the girl feel more relaxed, although if she's a bad un it will make no difference. However I have frequently had better service from those who don't count the money and put it away but just leave it alone.
In parlours the etiquette is usually to pay afterwards.