There is no “ordinary language” here.
This is a technical word. It has a technical definition. Ordinary people don’t use the word. Only people who appreciate the technical definition become advocates for the idea. If you have misunderstood until this point, that is unfortunate, but it is not incumbent on physicists or philosophers to make sure every interested lay reader is fully up-to-speed on every definition. You have to do the reading yourself.
The many-worlds interpretation has always been called deterministic. From literally the beginning.
The entire point of the MWI was to create a deterministic alternative to the Copenhagen interpretation. That it is deterministic was explicitly written in Everett’s original PhD thesis when he discovered/created it.
Your misunderstanding is personal. It is your mistake, not a mistake in the “ordinary meaning” of the word. I understand that it feels to you personally as if your meaning is the ordinary meaning, since you’ve been carrying it around in your head all this time and it’s been perfectly ordinary to you. But it’s not. You’ve been carrying around a misconception, and it is not a generally held misconception because this is not a generally discussed topic. Among the select people who are highly interested in the disputes about interpretations, it is perfectly common knowledge that the MWI is deterministic by the standard meaning of deterministic.
That was the “radioactive decay” article and it wasn’t written from the perspective of the MWI or any other deterministic interpretation. Copenhagen is still the most common interpretation. As with many Copenhagen-based explanations, it would have to be “translated”. The probabilistic predictions remain the same for all interpretations, but the underlying belief about the universe is different. I cited the article not for determinism, but to show another poster that radioactive decay is in fact a quantum process.
I can give you my own “translation” later if you’re interested. (But keep in mind, I’m not a physicist.)
In the meantime, here’s Sean Carroll talking about various interpretations. A 14-minute video.