I think perhaps two "uni"-verses is a bit misleading in what you seem to be getting at. From what I understand of what you're saying, it sounds like what if two big bangs happen in the same universe, but in very different places (and at possibly different times). The effects of each bang would be expanding outward at the speed of light (assuming nothing travels faster than this). Some people consider the size of the universe to be the sphere with radius equal to the age of the universe times the speed of light. By that definition though, the universe is expanding. (Into what?)
Now, if instead, we consider the universe to be all possible space that the effects of the big bang can spread into, rather than the area currently affected (due to radiation or matter passing through), it would seem possible that there is more than one point at which a big bang could occur. Since they start off in separate locations, there is some minimum amount of time before they would be able to "see" each other (in terms of radiation or matter from one interacting with the radiation or matter from the other). If this minimum amount of time has not elapsed, then you, being in one of these big bang affected areas, would not be able to observe or detect the existance of the other, because nothing (not even light) would have had the time to travel far enough. Now what happens when enough time elapses so that their sphere of influences begins to intersect?
I believe that's what the question was.
I think extra stars would just sort of pop into "sight", like someone turning on a light. Since the distance is so great, I suspect they would be so dim that you'd have trouble seeing them, and the increase in background radiation would be extremely minor. At least, assuming both big bang points are stationary. If one is moving in relation to another, than perhaps a Doppler effect would create a big flash of light/radiation, much like a sonic boom. But for that to happen, one would have to be moving close to the speed of light in relation to the other.