I've just discovered review and got two Custodian badges for it, sweet! But I never got a notification for them, as I did for every other badge, and only discovered them when I noticed my bronze badge count incrementing.
Most of the bronze badges don't notify users who are considered "veterans" of the network, which is (loosely) defined as having accounts on multiple non-meta sites.
The rationale is that getting a notification everytime you join a new site and, say, downvote gets a tad annoying after a while.
Custodian, being one of the "you did one thing"-bronze badges is one of those who's notifications are suppressed.
Not really an answer, just confirmation that custodian badges generate notifications:
Smells like a bug.
Although I just got custodian on Code Review, there was no notification.