I'm not certain, but can this be fixed by 'resetting' the document? You can try a few tricks for this:
1. Refresh the Zotero citations and see if that helps.
2. Copy/paste into a new document and refresh.
3. Change the citation style to something else and refresh, then switch back and refresh again.
(Before doing any of that, I'd suggest saving a backup of your document!)

Sometimes earlier settings/properties are maintained until a full reset occurs, and in order to save time processing Zotero doesn't automatically do a full reset except with major changes. It might automatically catch up also if you were to keep using this and it had to decide about for example a new citation from one of the authors.

(A less likely possibility is that you have an orphaned citation in your document no longer connected to your library, but that doesn't sound like what you described.)

If none of that can work, of course you should be able to go back through all of those citations manually and replace them (perhaps delete them then replace, rather than just editing), but that probably isn't necessary if you try the steps above.

There's no such thing as a "reset" of the document.

Unless you're suggesting different terminology, that's not entirely true. Sometimes just refreshing once doesn't completely reset everything. There can be some echoes of old settings. It's rare, but when something buggy like this happens, it's usually fixed it for me. Often switching between citation styles is the most helpful method, if simply refreshing doesn't work.
Of course I can't provide any more specific evidence or conditions for this, but more than a handful of times I've had something odd about a document fixed by more than just refreshing. And sometimes it seems like it eventually catches up if you just keep using the document. As I said, "echoes" of old settings. This happens for me sometimes, I believe, in the same situation as the OP, where I've updated something in my library and it doesn't immediately get caught in the normal refreshing of cites in a Word document (for example, the bibliography will keep being generated with the wrong information that I've already fixed in my library).

Sorry if my answer here is seen as disruptive or not a standard response. I'm just commenting on what's worked for me. And since this sort of "echo" doesn't ever seem to be permanent*, I don't see it as a big problem.
[*The exception would be if, as you said, the cite gets de-linked from your library.]

a Refresh should update all citations in the document that aren't in one of the two states I list above.

Yes, it should, but sometimes it doesn't. Sometimes refreshing twice does, not always.

As I say, there are document debugging steps that can be used if something isn't working properly, and those include trying to change the citation style. But it's incorrect to suggest that there's some sort of standard expected situation where changes wouldn't be applied on Refresh. That would be a bug, and we'd want people to follow the debugging steps in full so that they could isolate the problem in a copy of the document and report it so that we can fix it going forward.

Yes, you're right about that, and I didn't mean to interfere. But personally if I can 'reset' it by swapping out the style for another and going back, I'm fine with that and wouldn't want to bother you with debugging it if it's that easy to fix on my own. I'll try to remember to post next time this happens though if that helps improve Zotero!!

(I understand how it's supposed to work. I'm sorry for any confusion.)
I will gladly let you know if I encounter this in a way that allows a Debug ID.

If you still have the original document and can still reproduce the problem there, it'd be great if you could send an excerpt with which the problem occurs to support@zotero.org with a link to this thread. See the last step on the Debugging Broken Documents page for instructions to very quickly narrow down the document to a part that's broken.

dstillman is literally asking for specific information to help troubleshoot and fix this. If you want to help, you can provide those.

The error arises when fixing errors arising from single authors having multiple names/ spellings. When names are corrected in Zotero, a refresh fixes the bibliography, such that all author names are correct, but the in-line citations retain initials or first names, even though those entries are no longer in Zotero itself.

As with above users, swapping citation format and back fixes the issue.

@Allentl: This works in general, so to fix the problem you're reporting, we would need steps to reproduce it in a new document with new dummy items and/or an excerpt of the original document from before you fixed it (which you could send to support@zotero.org with a link to this thread).