How does time transform in wormholes? The light from a star 100 light years away takes 100 years to reach Earth so we see remote star as it was 100 years ago.
In the same way, we would see Earth 100 years in the past if we were on the remote star.
How does time transform if we have a wormhole connecting Earth to the remote star?  For example, if we leave Earth by stepping into the wormhole, do our watches need adjusting when we exit the wormhole at the star?
 A: What you describe in the first two paragraphs is not what a physicist would refer to as a transformation of the time coordinate.

How does time transform if we have a wormhole connecting Earth to the remote star? For example, if we leave Earth by stepping into the wormhole, do our watches need adjusting when we exit the wormhole at the star?

GR basically says the answer can be anything. You can have wormhole solutions that connect any two times. Wormholes are generically time machines as well. If you have wormholes whose mouths are synchronized in a certain initial frame, then they're not synchronized in another frame. Furthermore, you can in theory change the time difference between the holes by accelerating one of them around, which causes time dilation. That is, a wormhole that is not already a time machine can always be made into one. The original paper on this is Morris, Thorne, and Yurtsever, "Wormholes, time machines, and the weak energy condition," Phys Rev Lett 61 (1988) 1446.
