Overloaded with a fresh puppet

[Shinron-PUP]

Overload, in some techinical sense, does reset when you deactivate/recactivate your pet, but the affect, if still on, after overloading on your previous pet will still remain on the new one. In regards to your question, "What is the deal with overload not disappearing." It's not the fact that it isn't disapearing, but when your pet is activated, this is one of the peeking points in which overload is at its highest burden. Square Enix, with its notoriously stupid ideas, created the system to be where when your pet is Activated basically all attachments, that are job abilties, are down and overload is high in order to make it more difficult to do things spontaneously after activate because it would "Over power" the job in some sense. All though you do start off with high overload when your pet is activated, it does decay faster than normal overload would at any other time. Using this website will further allow you to understand how overload works if you look through it completely http://wiki.ffxiclopedia.org/wiki/Overload

So in summary... Overload does reset after deactivation, but when you activate you will begin with a new high amount of burden in which will decay completely in about 2 minutes of waiting, but if you have all the up to date overload gear and of course the new job ability (Cool down)... this won't be much of a problem and you can use manuevers right when you activate your pet.