You might be thinking that for ordinary humans, but I'm not ordinary and I'm not human. I'm leaning toward the static version you mentioned - we'd be returned precisely at the same moment we were taken, so for all practical purposed, it would be like we never left. There are people here from my past, and if they had been taken in a way different than what I described, that would cause a Temporal Paradox, disturbing the stream of Time and reflecting upon my present.
Curiosity might've killed the cat, but at least he had a fun time along the way?
I'm lording over Time. Duh.
I'm an alien from a highly advanced civilization that's mastered Time Travel and all its intricacies. And before you balk, remember, you deal with angels and demons, which I don't believe in the conventional way everybody else seems to do.
There's somebody here who says he is the Devil, Lucifer. Nice chap. He's been put in charge running a night club in Atlantis, which is pretty fitting for the Devil, I think.
Again, cheers. Field agents have recently been deployed, but they've been forbidden to tell us the where's and why's of their mission.