In the behavior forum there are often threads about proper and scientific introduction.
How is Riley, I suppose he is male. Is he a tom? Is he territorial tom or is he a cat friendly, rather docile tom? (observe, not so few territorial toms may be friendly to humans, but ferocious to everything they think is rivals).
If neutered, how long ago?
Ex homeless are often more used in interaction between cats then home raised cats.
Thus, they often have much easier to adopt to the residents then a home raised, bough cat.
A typical reaction is they are submissive to the residents, eager to please themselves in.
The big exception is territorial, non shy toms... They can often beat up the residents.
So that is why it is imperative to neuter them several weeks before you even think on letting them meet the residents.
Shy, not aggressive toms are much easier. :)
So that is why Im asking.
If your answers show he is neutered long ago, or a very cat friendly, non territorial tom - you can start rather sharply. No big need of waiting much longer, now when the quarantine period is over.
Make sure they all have nails cut. Make sure there are places to take shelter in the meeting room.
Let him (and the residents of course) make himself comfortable with the meeting room. One hour does suffice.
And let them meet.
You can preferably begin with the friendliest of the residents.
This should work good enough. But if you want to be thrice safe, take it more slowly and more scientific of course.
Vanilla on the base of tails, swapping smells, etc...
Good luck!