There seems to have been some strange issues with WK just now, a few users are also reporting problems with the site. Here’s another example of a similar problem, including a response from the devs: Repeating reviews (again) . So I suspect you are just running into those problems and not an app problem.
But I’ll answer your question about the syncing anyway:
If you’re online, every item is synced immediately as soon as you finish it, so normally your sync will be completely finished by the time you finish your session. If you have unlocks the app will do an extra sync after you finish the session just to make sure you see those unlocks immediately.
But if you are offline during the review session, the sync will only start when your device comes back online. You’ll have to open the app for a moment to kick off the syncing process (unless you have background sync enabled), but once it’s started it will continue in the background even if you close the app.
Usually, the only reasons for a review result to be rejected by the WK API is if you did the review on the site or another app already, or if your device time is set incorrectly.