More the other way round because the key press is the overriding animation. You want to play moving and idle whenever possible, so you add conditions to these animation events such as 'invisible is not playing', so if invisible is playing it will not play standing or idle until invisible ends, then return to playing either moving or idle.
In the specific case of your event sheet you can add second conditions to both the bottom events 'invisible is not playing' and it would be fixed but also trying to explain why it would be fixed.