Do you encounter a space after you teleported to another one on the same turn?

(i.e if you got 6 on the Shrine card you can teleport to any other space in the same region, will you encounter that space aswell?)

Yes, Dungeon has a few specific bits that cause you to move upon a defeat and Dungeon rules state in these cases you don't encounter the new space. But normally, you always encounter the new space or a character in that space.