You may want to check out some behavioral management resources. A good starting point would be the Handbook of Primate Behavioral Management (Edited by Steven J. Schapiro, he and the individual chapter authors can be found on ResearchGate), then look up some additional species specific sources from there.

Generally less time they are with humans better reintroduction works. I should suggest they are reared already at close contacts (visual and auditory) with adults of their own species. I think there are a lot on zoo-related literature on this issue.

If you want to maximise success you need to be patient. You should first house the hand-reared and captive group in adjacent exhibits so that they can see and hear each other easily but not touch. Do this until both groups seem settled by the presence of the other. Then remove what barrier prevents the primates from touching, but make sure to keep some sort of mesh between them so that the hand-reared individuals can retreat from contact if they want to. At the beginning you will need to supervise this physical contact between the groups because the captive animals might try and pull the arms/legs of the shyer hand-reared individuals through the mesh. Hopefully, eventually, the primates will start grooming each other through the mesh, at which time you can remove all barriers between contact. There will be squabbles and fights at this stage when there is free movement between groups because the hand-reared individuals will need to establish their position in the hierarchy. You should allow this to happen, within reason, as it is an important social skill the hand-reared primates need to learn and only when they have established their rank in the hierarchy (even if it is at the bottom) will they be fully accepted. Of course you can try shortcuts to this approach, but the whole process will be far more traumatic for the hand-reared animals and much more disruptive to the established captive group.