A transition is done when the object is shown or hidden. Your groups are not “initially hidden” so the groups / objects are shown when the page is loaded, delayed by the tranisition. Your “Transition Out” would work but you have to hide the groups with an action. If you add a delay to the transition, it would mean that the transition starts n seconds after the Hide action is run.
You can add a transition out to the groups (without delay). Then add an action to one of the objects in the group:
Target: Respective group
Delay: 4.7 sec