So for this card Chaos Rift, I was wondering if you encounter the new terrain card that gets put in your space, the same turn that it gets placed there.

Title: Chaos Rift

Card Type: Event

The world shifts and tears.

All characters roll 1 die. Each character with the lowest result must place 1 random Terrain card on his space. Then discard this card.

Encounter Number: 1

You wouldn't encounter it. There are some cards that specifically say, "Put a terrain card on your space and then encounter it." Plus, if everyone had to encounter their terrain cards that turn, it would get everyone's turns confused.

I think he means does the active player encounter the newly transformed space, I would agree not.

No.