²⁰⁹Bi decay to ²⁰⁵Tl is alpha decay — the bismuth nucleus splits into an alpha particle (helium) and a thallium nucleus. I think you’d be hard pressed to find a nuclear physicist or engineer who calls that “fission”.

Here’s the Wikipedia article on fission. It’s a rather different process:

https://en.m.wikipedia.org/wiki/Nuclear_fission

Maybe the fault is with me for using the word "reactor" a bit loosely.

I don't think anyone knows for sure what is going on down there.

My theory is that it's both critical and quiescent, with a violent dynamic at play. Gravity will concentrate the heaviest and least stable elements as you'd expect. As that happens pockets of dense matter in close neutron proximity will approach critical and heat billions of tons of matter which then convects outwards, dispersing the mixture. Think of a lava lamp.