Note: the feature is still under development. This answer risks being out-of-date the moment I post it. For up-to-date information, see the MSE post "New onboarding for review queues".
Is this a bug? Is this a new feature that everyone sees?
It's a new feature that everyone sees first time they enter a specific queue. You'll see it (at least) once per queue, per site. Meta sites have their own queues, you'll see it there too. So if you'd have sufficient reputation on all 177 or so sites, yeah, that's a lot of modals you'd be seeing.
But more importantly, have I done something wrong during reviews that led to this pop-up on my screen?
No. What happens is that the system doesn't check that you've done all those reviews. Not that it cares, because the design philosophy is that even people who have reviewed a lot already may not have been doing it correctly so far. So SE decided to just show it to everyone.
The new feature isn't flawless, so please report your bugs at the MSE post linked at the top of this answer. One of the current bugs is that even moderators are shown they have a daily review limit of 20 tasks per day, so take all information shown in those modals with a grain of salt.