Before you lock the anchor nuts, RETIGHTEN! Don't know the mechanism, can't get any good guesses from the eng's I've talked to but:
After the first tightening of anchors in concrete, especially cast-in-place anchors, they loosen themselves up. After the vessel/tank has had a few days after being full, per MJCronin post above, go back and Retighten, then lock the nuts [if you wish].
Don't overthink the 'Snug Tight'. For smaller stuff, it is "Full effort of a man on an ordinary [spud] wrench". For bigger stuff [like anchor bolts], it is "A few blows of an impact wrench". Put a wrench on the nut, hit it a couple of times with an ironworker's 'beater' [4# to 8#], keep hitting until the nut stops turning and the hammer just rebounds, and you are done. Rinse and Repeat.