here's the way i understood it (i did some research and watched it multiple times)
firstly there are two universes in this move, the tangent universe, and the primary universe. The primary universe is the universe which we are all living in, the tangent universe is the universe that is parallel to the primary (a lot of the movie takes place in the tangent universe.)
now the jet engine flies through Donnies room, this is a spontaneously appearing item which is a sign that the tangent universe has been created. at this point, the tangent universe is an exact copy of the primary universe, they are parallel.
the tangent universe has chosen donnie darko as the reciever of the jet engine, which he must return back through the portal.
https://www.newschoolers.com/ns/forums/replythread/thread_id/156393/
frank (the rabbit) has died in the tangent universe, so he goes back in time to help donnie return the engine. frank is the manipulated dead, since he died in the tangent universe.
the manipulated living are all of those who are connected to donnie (since he is the chosen reciever).
the manipulated living aid in the return of the jet engine.
at the end of the movie, donnie ends the tangent universe (which has been going on for 28 days) by returning the jet engine. now that the tangent universe is over, the primary universe resumes from the point before the 28 days.
another note, once the tangent universe was created, the 28 days were set in a parallel or alternate reality. if you notice, all the characters seem to be living as if they have already lived those moments before (as if the 28 days have repeated). also the tangent universe was not created by the jet engine, the jet engine only flew from the primary universe into the tangent, as an artifact that must be returned. the creation of the tangent universe was not explained during the movie.