what time zone do wow realms run on?

Depends on the realm. Each one has a time zone listed next to it on the realm selection screen, the NA ones are a mix of Pacific, Mountain, Central and Eastern, and Oceanic realms run on Australian time. The in-game clock can show realm time or your local time, there's a toggle for it on the clock. If what you actually care about is the weekly reset, that's region wide rather than per realm: Tuesday morning for the Americas and Oceanic, Wednesday morning for Europe.