Does crossing a wormhole happen instantaneously, or with the course of time?
I have seen many science fiction movies that depict traveling in space through wormholes. The appearance though, and the time it takes to cross a wormhole, tends to vary:
Now, as far as I've seen, crossing these wormholes takes a few minutes or hours, but sometimes it takes years. However, it is said that while crossing the wormhole, even if it takes thousands of years for you to cross, in real time you get to your destination in no time.
Now, I'm designing a civilization of technorganic aliens that travel space using wormholes. Since I want my story to be as close as possible to real science, which one of these wormholes is closer to reality, and could they both be possible? If not, why? And if yes, how?
Edit: I'm editing the question to explain how theses wormholes of mine work. The idea is that a wormhole opening devise is placed on the front of a spaceship, that launches a small projectile (about the size of a baseball bat) in front of the ship at high speed (the speed of the projectile is faster than the ship so that it won't collide with the ship moving forward). When it activates, it creates a small wormhole which it makes bigger by adding exotic matter into it, stoping the wormhole from collapsing in on itself until the spaceship makes it to the other side. The wormhole will close after the projectile that created the wormhole runs out of exotic matter; the ship though has already crossed.
It should be noted here, that, if the second form of wormhole is the correct one, the wormhole will remain open to the "driver's" perspective, since to him the trip takes ages, yet in real time the trip took almost zero time and the wormhole closes shortly after the ship exits the wormhole.