Presidents have to pay for various personal expenses incurred during their stay in the White House. Only meals for state functions that are prepared by White House chefs are paid for by the government.
... when his family and personal guests eat what's coming out of the kitchen, he'll have to foot the bill himself. Luckily for him, though, the government picks up the tab if he's having a state function at the White House, which could get pricey since the White House's website touts that its five chefs can crank out dinner for 140 or hors d'oeuvres for over a thousand people.
Since the meals weren't prepared by the White House, the President can choose to foot the bill. There aren't any rules preventing Presidents from spending their own money on White House functions.
In general, Presidents also have to pay for groceries and other personal necessities.