To me, there is no question about it.  The envelope has to be counted before the fun begins.

When I go to the bank(or ATM), I don't leave the teller station until I've counted the money.  I'm not trying to insult the teller, its just that mistakes can be made.  

I don't think this was a mistake, but no one will get insulted by you checking the money unless they are up to no good.  Don't make a spectacle of it, just quickly review the contents.  If there is a mistake(like $20 short, discretely mention it).  It its more than 1 bill short, then I'd give them the envelope and leave, without starting a confrontation.

From what I've learned in my short life, its ridiculous to think you should trust everyone to do the right thing.  90% will do the right thing, but you can't always immediately identify the other 10%.

Just be safe.

It sounds like you provide your service out of a residence. One thing you may consider is if you accept your gift via an envelop (make sure you inform them not to seal it prior to the visit), is to have the gent place it on a table outside the bedroom. When you escort him into the bedroom to make himself comfortable, close the door and excuse yourself from the room briefly to check the donation. If everything is cool, then the fun can begin. If for some reason the required amount is not there and the warning bells are going off (might be LE or ripoff artisit), go back in the room and indicate you just got an urgent page from a family member requring immediate assistance and the session can't take place.