Whenever somebody calls LLMs "non-deterministic", assume they meant "chaotic", in the informal sense of being a system where small changes of input can cause large changes to output, and the only way to find out if it will happen is by running the full calculation.

For many applications, this is equally troublesome as true non-determinism.

That's not really true. If you turn a few knobs you can make them deterministic. Namely setting temperature to zero, and turning off all history. But none of the cloud providers do this. Because it's not a product as far as they are concerned. So in practice - not so much.

Yes theres a good thinking machines lab blog about this

You're being downvoted, but you're right. Determinism is a different concept and doesn't characterise LLMs well. You can have deterministic random number generators for example.