There may have been more to the vaults than has been said. Perhaps the overseers didn't know that bombs had actually fallen. They may have been told by Vault-Tec that the nuclear exchange was a ruse to allow them to start the experiments. I prefer to think that Vault-Tec somehow started the nuclear war in order to get people into the vaults and to start the experiments. The overseers might have been overseen by a secret overseer who made sure they carried out the experiment. Vault-Tec may have had a central vault controlling all the other vaults.
Actually, the only way the Vault experiments make even a little sense is if Vault-Tec
never expected nuclear war to actually occur.
I get the impression from some of the terminal notes in a few Vaults that they were indeed occupied and sealed before anyone knew the nukes were coming. It would have been a simple enough thing for Vault-Tec to tell these people that were paranoid enough to spend vast amounts of money reserving a space in the Vaults that the bombs were on the way and they had to get inside quickly. Vault-Tec could claim advanced knowledge or sources for the info, and people would believe them, not being able to risk staying outside the Vaults.
The music Vault is a good example. It seems from the diary notes you read on one of the terminals that the person was offered a spot in the Vault and had time to mull the offer over and then pack up her cherished possessions (like a violin) and enter the Vault.
Vault-Tec is just as bad as the Umbrella corporation in the Resident Evil series if they truly jeopardized the future of the human race for some silly experiments. (Will Mormon's freak out if they have to live naked? Will children form a society by themselves with no advlt supervision or go all Lord of the Flies? What happens when we bore people with no entertainment? What happens when we entertain them with lousy comedies? Etc.)
I firmly believe that Vault-Tec never expected the Doomsday Clock to hit midnight. Some of the overseer notes seem to indicate that the overseers follow the experiments because they believe that no bombs fell and Vault-Tec authorities are standing by outside monitoring the activity in the Vaults. Maybe the best indication that Vault-Tec never expected the bombs to fall is that we find no Vault-Tec employees in any of the Vaults, and none seem to still be alive on the surface either - even Vault-Tec HQ is abandoned.
Mostly though, I think the Vault Experiments are a pretty stupid retcon based off of only 2 lines in Fallout 2 (one from the President and one on a computer terminal) and then taken and run into the end-zone by Chris Avellone in the Fallout Bible. The things that are considered official experiments are stupid. Penny Arcade's Fallout strip of one guy and a crate of puppets is considered canon?! I love Penny Arcade, but what the hell? Men, women, and one panther? One man and a 1000 women? Jesus, was the Vault-Tec CEO an 8-year old child?