There's an entry in some terminal or a dialog or something that explains it? Same goes to Vault-Tec.
And if they have researched and developed it before the war, why wait for 2178 and behave like FEV is discovered only now?
Because the Institute's divisions are autonomous and it's more like a confederation of independent parts than a cohesive, whole faction. There are secrets within secrets, shrouded within secrets in the Institute. In the horror and chaos of the Great War, who would notice that a file on a top secret, eyes-only project disappears and a sample gets removed to a reinforced location?
For Vault-Tec, it was apparently intended for it to be set up around Wayne Merrick, for a rival research effort:
I'm told that Dr. Merrick is one of the brightest minds in the field of accelerated evolution, and apparently
Vault-Tec agrees, because they've set up this Vault around him to suit all of his needs in the event that the bombs fall. All of his data and his work have been transferred to this facility from many important sources such as
Mariposa Base,
West-Tek and
Vault-Tec Labs.
I like Dr. Merrick. He's driven without being careless. He knows that in the event of a nuclear war, he may be the only person left in the world that can advance human genetics beyond where they are now. He's meticulous, detail-oriented, and reports everything to me on a regular basis.
More interestingly, it seems they already started experimentation before the Great War:
The latest subjects in the
Evolutionary Experimentation Program (EEP) are showing some promise after only a single exposure to the modified FEV. We are currently testing five subjects, two males and three females. Each one of them is under 24 hour observation as usual. We hope to have a breakthrough in this strain as the continual pressure from Vault-Tec and the military at Mariposa is becoming most bothersome.
http://fallout.gamepedia.com/Vault_87_terminal_entries
I don't like Fallout 3's writing, but there are interesting inferences to be had from available content. Vault 87 was a way to store a backup of the FEV project in case of a nuclear war... Except everything went sideways when the Vault was nuked. For all we knew, it may have even been deliberate, as a decoy protecting Mariposa. Given the degree of Chinese infiltration in Washington, D.C., it would also explain why our favorite military base escaped nuking.