In both cases they were hunted by the Monster, who seems to have a tendency to take his victims into the Upside-Down before finally making use of them. It was quite logical in case of a deer: there was a portal open in the tree, the Monster took the deer through it to the Upside-Down and ate a deer over there.
Say, with Barbara it is still explainable: the Monster opens a portal in the pool, Barbara falls there, ends up on at the bottom of the pool, tries to escape, gets caught by the Monster. The question still remains: why would the Monster give her some time in the pool after it takes her to the Upside-Down? Barbara seemed to be unconscious there for a little while before trying to escape. An obvious explanation is that it's better for a show, but I wonder if there could be an in-the-universe reason for this fact.
What I don't get completely is that Will gets a rifle (which we know is of little help) waiting for the monster, and then somehow ends up in the Upside-Down. If the Monster brings him over there (physically), how does Will manage to escape?