Regarding you're pets perhaps you've placed them and simply moved to far away. I derp this occasionally place my pet somewhere so it can cover the whole group during a boss and then move forwards through the instance forgetting to tell it to "heel"

as for hotbars there's also quite a few settings that will automatically change sets such as always going to set 1 if you put your weapon away. always going to set 2 when you take your weapon out or engage a monster. these can cause issues when you're trying to cast spells in the few seconds between pulls and things... perhaps worth taking a look at.

that said though I do rarely get occasions where I tap the stick to dodge an attack and find my character continues to move. at first I thought it was just me catching l1 (autorun) ever so slightly but happens with any of the controllers I use. and only ever on the pc. I did at one point completely remove all my controller drivers and reinstall them, and haven't had the issue since. (thus far at least)