Basically, using a newly tamed pet, a stopwatch, and a notepad, she determined that in order for a pet to go from loyalty level 1 (Rebellious) to level 2 (Unruly), the pet needs to gain 5% of the experience the Hunter needs for his next level. So a level 11 hunter needs 8800 experience to get to 12, which means a pet (of any level and family) needs to kill for 440 XP (5% of 8800) to go up a loyalty level with that Hunter.
Interesting. And the formula apparently works even when the pet isn't actually earning experience (ie when your pet is the same level as you are). However (and this is a big however), time is also playing a factor, and Mania's not exactly how it does-- she let her pet sit happy for a few hours, and then on the very next kill, the loyalty level went up. So it seems to be some combo of experience earned together and time (where more experience or more time can replace the other if necessary), but the exact numbers aren't there yet.
At any rate, good stuff, and Mania is being really thorough with it. If you're a Hunter who changes pets often, it's worth a read.