Official comment
It shouldn't "move" the cue marker when pressing the cue button, typically it requires the deck to be stopped (pause mode).
Are you able to replicate this regularly or was it a one-off problem?
As for the track playing on load, I'd recommend turning on the auto-cue in the rekordbox preferences - that would automatically set the master cue at the start of the track (or first hot cue, depending on your setting), and stop playback at that point. (Just a personal preference, but you may want to check it out.)