Basically the same way Trump bills his own secret service for millions when he stays at Mar a Lago.
Just for the record..I used to play golf with someone who was with the Secret Service. Who then went on to be a local Director of Homeland Security. ( and btw, he always had a suitcase packed in his boot with his necessary weapon as well, in case he got a call to report at any time)
They get paid regardless. What someone in the Secret Service prefers, is a job away from their home location. Then they get to claim expenses. If it's local, they receive very little in the way of expenses.
The President being based in Washington DC has a specialized Secret Service crew. Anytime the President moves out of the Capitol, regardless of whom that is, they get their expenses taken care of. Same with the Vice President.
Also, all Ex-Presidents and their families have Secret Service protection as well. So do the Senate and House of Representative majority leaders. ( Currently McConnell and Pelosi ).