A fossil Pokémon IV's are determined when they are given to player, not when they are revived.
So for example if I wanted an Aerodactyl with 31 IV's in Attack and Speed and I saved the game before the Scientist gave me an Aerodactyl (that they revived from Old Amber), if I soft reset my game and talked to the Scientist again the Aerodactyl they give me won't necessarily have the same IV's as the Aerodactyl before.
It's the same case as receiving an Egg from the Day Care Man, if you save the game after he gives you the Egg even if it's not hatched, it's will also have the same features. However if you save the game before he gives you the Egg, you can just turn the game off if you're not satisfied with it's features and hatch the Egg again.
Let me just clarify though that a Pokémon's Nature, IV's, Shininess, Characteristics, Gender, Ability etc. are determined when the Pokémon is given to the player.
Source: Experience and Knowledge.