That's my understanding as well, except ..

Old users will always follow the most difficult chaintip and don't need to choose afaict. They can spend their money according to old consensus rules and it's compatible with either chain ... and given enough time, it should be mined on both chains.

The old/upgraded miners are at risk of mining on the wrong tip though, and upgraded nodes that declare non-upgraded blocks as invalid are at risk of accepting spends that only appear in the upgraded blocks (which may be re-orged out).

It's worth getting up to speed on this stuff because it'll be the first forking season for most of us.