Allen Mack has taught basic survival skills to his children but isn't overly fond of showing emotion. Should the previous overseer, Alphonse Almodovar, ever become incapacitated, Allen has vowed to take over the running of Vault 101.
During the quest Escape!, it is impossible to enter the room where the Macks live (without cheating or hacks). Viewing Vault 101 in the G.E.C.K. reveals that Mack's 'room' is just a short stretch of corridor without entrances. It is impossible to enter his room due to the fact that he is scripted to become the new Overseer should the current one die. This preserves the storyline for Trouble on the Homefront.
One of his combat lines include "The Overseer will hear about this!", even after he becomes the Overseer.
Even though he and his wife are Asian, their children are all Caucasian.
It is possible that they adopted all three of the children, but if the kids themselves are related it is unknown.
Even if Mack becomes the Overseer, Amata will still refer to the Overseer as her father.
"What's the matter, runt? Did I hit a sore spot? I always knew we shouldn't have taken him in, and it looks like I was right all along. A perfect example of why we need to keep the Vault shut! Now, I'll make this easy for you. You can walk away and let me handle the Vault, or I can put you down like a rabid dog. Your choice, kid."