Ok, I've searched the forums and haven't found anything relating to my problem so here goes.
I brought the water chip back (and lost poor Dogmeat in a fight with supermutants (possible reload)), and talked to the leader of the vault who sent me to the library. Now, not only do I wish I'd talked to him about letting people out of the vault (all part of the game I guess) but on my Pipboy, under "Vault 13," it says I have also completed "water thief" and "calm rebellious faction" along with the water chip mission.
What gives? Is it a time limit thing?

Those quests are to do with the water shortage.

You've returned with a working water chip.

Hm. Acknowledged. Now I'll try going back and doing those missions before returning the chip. Hopefully with Dogmeat.
Thanks!