For the first half to 3/4 of the game from our perspective, travel through the temporal Gates is carefully controlled by some willful Entity for a purpose the characters can only speculate on
And I appreciate that neither CT npr CC make it 100% clear what the rules are because the characters don't have the means to figure that out. They just do what they can.
if you would, upon learning that you time traveled, refuse to time travel in order to cause a paradox, then it won't work for you