If I have zhonya’s on base and two units in combat at a BF with one of them being tank and they both die in combat damage, does the tank unit get the zhonya’s effect or do I still get to pick?

You still get to pick. Tank only controls how damage is assigned, not who Zhonya's saves.

Damage assignment (Tank first) happens in a specific order, but the damage is all dealt simultaneously, so both units become "would die" at the same instant. Rule 373 treats simultaneous events separately, and the controller of the replacement effect chooses which one Zhonya's applies to — so you may save whichever unit you want, including ignoring the Tank unit (FAQ #1042).

One requirement: Zhonya's must already be face-up when the damage happens, since it's a replacement effect and not a trigger. If it was hidden, you have to flip it during the Showdown while you have priority — you can't wait to see which units die. Whether it's in your base or at a battlefield is irrelevant.