And thus that there is no “countdown clock” on an atom determining when it will decay.
Only if you change the word “deterministic” to mean something else that what it means in ordinary language.
In ordinary language, a “deterministic” model means that this here atom has an “expiration date” attached to it somehow, and that when that time comes, the atom will decay. This means there has to be some kind of timing mechanism, some internal clockwork, and a means of measuring time.
“Deterministic” in this sense is according to the “predestination” idea. It was fated from the origin of the cosmos that I would stub my toe against the chair leg on this date at this time. Ouch.
You seem to be using the word “deterministic” in a way that doesn’t mean that. I think it’s damn shoddy of physics to make use of words in ways that contradict their “ordinary world” meaning.
The “many worlds” model is not deterministic in the ordinary meaning of the world, since we have no way of knowing if we’re in the world where that atom decays today, or in the world where that atom decays a year from today.