Rut's absolutely right on this. If this happens, you should immediately confer with your partner to see which happened first. The "which" I refer to is the actual travel vs. the recognition by you of the request for the timeout, not which whistle came first.
Remember, your goal here is to get the call right.
OK - now what if you and your partner determine they came at exactly the same time? That's why some refs keep a coin in their pocket. We tell people it's to keep track of possession, but this is what it's really for.
BTW - if a howler monkey tells me I "can't see" after a game and I'm still on the court, he gets a T. Gee, wouldn't it be too bad if it cost him the game. Gee.