Where is Tahm Kench from?

I'm guessing Bilgewater. But we'll have to wait till his "lore" (more like one vague paragraph) comes out.

Bilgewater.

He doesn't sound like an undead thing

Given that he's basically an over-sized amphibious catfish, it's likely some kind of wetlands area. So I'd suspect it's more likely he's from Bilgewater than Shadow Isles - or someplace we've never heard of before.