"instance of time" vs. "instant of time"

An instance is a particular example of something. This is an instance of an answer on EL&U.

An instant is a moment, an infinitesimal point in time.

Now, every instant is indeed an instance of time, because every infinitesimal point in time is an example of a time. There's a subtle difference, but it amounts to the same thing in some cases.

The overlap between the two is very small though.

It would be unusual to think of it this way though, unless perhaps you were someone who often thought about different examples of things moving through time and how they were alike or different from each other. In other words, unless you were a physicist.

It's much more idiomatic to say "instant of time" or simply "instant" when you mean such a point in time. I would recommend it.

If however you were taking several readings or measurements of something, then you would have several instances, and in the case of physics these might very well be of time. Here "instance of time" is the only correct one. Which is probably what leads these physicists to say "instance of time" when the rest of us would more likely say "instant of time".