Do I need TPMS sensors for a second set of wheels?

You need them if you want the dash warning to stay off. US-market JDM cars have TPMS, and the system expects a sensor in each wheel, so a bare second set will trigger a persistent low-pressure light. The fixes are to move your sensors over at each swap, or, far easier, buy a pre-programmed set that lives in the track or winter wheels permanently so swaps are genuinely bolt-on.