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Yes expansion is meant to apply to spacetime, i.e., space and time which Einstein showed are different aspects of the same thing.
If the expansion is allowed to continue unimpeded then for time that means a "kind of" slowing down and an eventual stop. I say "kind of" because things can only really slow down if someone with a stopwatch can measure that slowdown. But in this case the stopwatch would be slowing down too...
The concept of time has to do with the ordering of events and, in practice, with relating the frequency of seemingly regular events to other more random seeming ones. But when all things get far enough apart and there are no observable events left at a given location in space then time ceases to have any meaning there. But there can be no one there to appreciate the end of time, because if there was then their very existence would be defined by a series of many events and their order, and hence time.
Time cannot exist where nothing ever happens. It's kind of the other end of the breakdown of physics in the Big Bang picture: the distant future... As opposed to the distant past, the event of the Big Bang itself, which cannot be understood, or more precisely, makes no sense in the context of our current understanding of the physical universe.
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