In other words, as Carol travels 'forward' in Bob's time, her clock runs backwards. Or, from Carol's perspective, Bob's clock would be running backwards.
This isn't actually a problem in relativity, but is the definition of time travel.
However, in the four person example, Dave is able to hand Carol her diary of the trip that she is about to make. If that is not time travel, I do not know what is.
The only reason that this cannot happen is that X and Y are so far away in space, and close in time, that it is impossible to travel between them.