interesting.Looks like you didn't use the whole hour the last time the pet was out.
I've found it rolls over and doesn't reset each day if you haven't used the whole hour.
Sort of the same as Alacrity scrolls do.
With most pets you only get to do it once.You take your pet to Chaos Shrine, yell: NUM NUM NUM" and pull its testicles, twice!
As ive noticed it, if you take out one pet and starts the training so it gains - powerhr starts. If you decide to switch pets during that hr - you get msg that the powerhr is over. So, I think its per char. Now if you stable and log out - maybe you just pick up the remaining of the last powerhr, like it is with whispering.As soon as your pet gets it's first gain, power hour for that pet starts. I suggest training for the entire hour so you don't get confused. It's per pet, not per character so completing the full hour is wise.