If space is always expanding, I’d really like to know if a time traveler would experience issues existing in a universe where the space between atoms is different from the one they left.
More importantly it's the electromagnetic force that keeps atoms together. Gravity only keeps planets and stars together and also solar systems and galaxies, but in ordinary objects it's totally negligible.
The big rip concept comes into play when the expansion rate starts to become faster than the forces holding molecules and atoms together. As far as current cosmic expansion goes, it only applies to space between galaxies. The current expansion rate is so weak it's not enough to overcome forces that hold galaxies together.
The big rip scenario happens in the case where the rate of space expansion is increasing. It's possible, but we haven't seen any evidence of it yet, so far the rate appears constant, which means a heat death scenario.