I took a look at this list of games containing time travel and went through some of the games that dated back to the 90s. There are youtube playthroughs and intros for most of them. Not that I've personally played any of these, but if it turns out that Myst is not the game you're thinking of, it might be either a game from "The Journeyman Project" series (probably the first one), or the "Time Commando" which while it didn't look like a first person game, the intro fit the description.

If it's not any of those games, that list is a good place to start looking:

http://en.wikipedia.org/wiki/List_of...ng_time_travel