I thought it might follow backwards in space as well as time but when the book The Physics of Time Reversal by Robert G. Sachs came out in 1987 it made me skeptical of that possibility. I haven't followed the theory of CP violation for many years so this may not be a pertinent point anymore.
For most "time machines" you read about, you aren't really going to run into the "CPT" issues from quantum field theory.
Unless you're considering a model of time travel where you're still literally in the same room and just living in reverse (while still visible to all the forward-living people around you and interacting with them as you go), this isn't equivalent to CP symmetry reflection.
Most time machine ideas instead picture some sort of wormhole or "stitching" between different points in space-time, in such a way that the local "forward time direction" remains continuous for observers taking the trip (and then connects back up with forward-directed time at some point in the past).
(I'm teaching a low-level course on "Time Travel in Science and Literature" this term. It's fun, but a challenge without using math.)
