From other clues, I'd guess that Rose's memories are not the result of a single information dump, but that the metacrisis somehow created an ongoing bond. That is because in addition to Karvanista, there are other references to things that postdate the Tenth Doctor's run. The workings of the metacrisis are only very hazily defined but as "weird Time Lord stuff" there is a lot of scope for weirdness in how it might manifest.
I think that this toy (held by the Meep at about 19 minutes in) is meant to be an Atraxi.
They appeared in The Eleventh Hour (here at about 47 minutes in).
That episode is the debut for the Eleventh Doctor and is also the first appearance of this species. They don't seem to have encountered each other before (the Atraxi don't know who he is; he doesn't call them "Atraxi" until after Prisoner Zero drops the name, and gives no sign of recognition).
In the scene where the connection is explained, and we see the various toys, the Cyberman one is accompanied by a voiceover saying "Upgrade in progress". This is from the Eleventh Doctor episode Nightmare in Silver, although it's also a fairly generic new-Who Cyberman thing to say (close to their dialogue in Rise of the Cybermen / Age of Steel).
The BBC put out a behind-the-scenes video ("A Tour of Rose's Shed") which pairs the toy from the question with an image of Karvanista (at 1:10). So this is certainly meant to be him. (The same video identifies the image above which I thought was an Atraxi as a Dalek, but I think that's a mistake given that the episode makes a different blue toy be the Dalek.)
In the series, the Thirteenth Doctor is supposed to have known Karvanista long ago but had the memories removed. By the time she encounters him in Flux, she's not aware of the connection between the human and Lupari species, which would suggest that there aren't any off-screen encounters between the Doctor and the Lupari in the interim.
The following sketch from the "Rose's Shed" video did not make it to the episode, but is indicative of some loss of fidelity in the memories or sense-impressions. This shows something about how the production team thought about what is going on with Rose's images.
Here we see a sort of hybrid of Karvanista, the Eleventh Doctor, and Davros. This hasn't happened in the series - yet. But it is consistent with Rose getting a rough idea of stuff that's been happening to the Doctor. At least two of the elements (Karvanista, the fez) are things that the Tenth Doctor ought not to know about. The fez appeared for him in The Day of the Doctor but that likely took place after Journey's End and he is not meant to remember it afterwards in any case.
The Lupari appearance could be interpreted as any of -
- A long-buried memory from a pre-Hartnell Doctor. But these memories are supposed to have been erased.
- An offscreen encounter sometime before the events of Journey's End when the metacrisis took place. But if that happened, the Doctor seems to have forgotten all about it by the time she met them again.
- Their reappearance during the Flux event. But this is after the metacrisis was formed.
Given the other clues, especially the Atraxi, I think that (3) is actually the most likely. For this to work diegetically, we'd have to imagine that the metacrisis entails an ongoing connection between the Doctor, Donna and Rose - tenuous enough to give Rose an impression of these creatures but something short of her having detailed knowledge of the Doctor's adventures.