Welcome to Android Central forums. I'm not sure if I'll be able to help but just a few things about your post.
You say you organized them with sync turned off. I must assume that you turned it on, perhaps after the organization, did they revert back to the old order on the PC?
It has been some time since I've used a tab, but is the tab browser like a desktop browser in layout? I thought it was still a mobile version of the app.
Anyway barring all of that, did you do anything like use "sync now" when you were complete or when you opened the tab browser? Not that this answers your question but FYI sync is a weird thing. There appears to be little rhyme or reason to when it occurs. If you didn't actively say sync when you were finished it may not have synced yet. It isn't usually instant, not even when waking up from being offline. It can take anywhere from a few hours to a day for some items to sync. As for where does the sync come from I cannot be certain however I would have to say that Google just looks at the last device you were logged into and using and syncs that with whatever you're currently on. I think that would have to be the way that it does it otherwise you would have to repeat everything on one device in order to have the sync. What I mean is if it were one device that Google pulled from to sync, the way your question is phrased, only whatever on that device is shared with the other places you log in and they wouldn't share with that device. It would be a one way road.
I'm not sure how you organized these bookmarks, but perhaps try with sync on while your doing it instead of waiting until afterwards, is the only thing I can think of. The other thing that comes to mind is, how are they organized? Is there any rhyme or reason to that? I mean are they alphabetical, by date, by most visited or most recent? Perhaps look for other options in how to organize them in the settings. It may not be possible to just create any old order but then again I don't know how you're doing this.