"...if the matter that enters a blackhole [...] is teleported through time and come out when the black hole evaporates in that distant, extremely dark universe."
Probably not. A BH (black hole) can emit all sorts of particles via Hawking radiation, but the odds are that most of the emitted particles are photons. For stellar mass & larger BHs, those are very cold microwave photons corresponding to temperatures around a billionth of a degree above absolute zero, and even colder for the big ones at the cores of galaxies. And the emission rate is also microscopic, so even if we had a BH for convenient observation in our solar system we'd have great difficulty detecting its Hawking radiation.
If you want to play with the numbers, take a look at the Hawking radiation calculator by Viktor Toth.
Of course, in the present era all such BHs are much colder than the CMB (cosmic microwave background), so they absorb more radiation than they emit. In the far future, when the CMB is less than $10^{-9}K$, and the BHs get a chance to lose mass via evaporation, then they may emit the occasional electron or other low mass particle along with the photons.
Bear in mind that we need a working theory of quantum gravity to give proper answers to questions about what happens inside BHs. Even Hawking radiation is a bit shaky, theory-wise. For that matter, we still don't have first-class observational evidence that BHs exist, although we're fairly confident of lots of BH candidates, and if they aren't actually BHs, then they must be even weirder. :)
But anyway, we're fairly sure that normal matter cannot exist inside a BH. It gets spaghettified on its way to the BH core (which may or may not be a mathematical singularity); even atoms get ripped to pieces. We don't know what actually happens at the core, but many theorists expect that some quantum effect prevents the core from having zero volume. See Ben Crowell's description of what a BH singularity is like, according to current (non-quantum) general relativity.
So a BH core is very unlikely to preserve matter as we know it, and when a BH evaporates, it mostly emits photons, at a very slow rate... until it gets small enough to evaporate explosively. But as I said above, we don't yet have a working theory that we can use to model the final phase of Hawking radiation, so who knows what can happen then. ;)
Your question mentions micro-black holes. It's possible that such things were created in the very early universe, but if so, we haven't seen any evidence for them (like gamma ray blasts of Hawking radiation as they die). And we have looked for them, since they're a possible dark matter candidate. We don't know any process that could produce them in the present era. There was talk a few years ago that they might be made in a collider like the LHC, but only if certain non-standard gravity theories were correct. It was unlikely then, and since then various other observations have made such theories even less likely,
