For Tigerstar, the effects would probably be the same--the mushi can affect any dreamer, but it's mind-blurring properties are more prominent in creatures with a firmer sense of self-identity. The mushi do encourage a longer sleep cycle, but within three days it would not unbalance a natural sleep cycle any more than an ill-advised all-nighter might.

As for interrupted dreams, anyone that was in a dream whose host has woken up would simply be pushed into a new dream, with the sort of transition one would experience going from one dream to another in their own mind. Dream-walkers can also wake and exit another person's dream at any time.