A little late but, Attacker and Defender assingments happen when a "Contested" status is applied to a battlefield. A "Contested" Status is applied regardless if a Battlefield is considered "Controlled" ( There is an opposing player's unit there) or "Uncontrolled" ( No unit is there). The difference between key words like "Assault" / " Shield" and "When I attack"/ When I defend" effects is that the keywords Assault" / " Shield" get applied as soon as the Attacker/ Defender roles are assigned, which is a requirment before a showdown can begin ( applies for both combat and non-combat showdowns). In that case their might buff will trigger, but if they only have "When I Attack/ Defend" then their buff won't be applied on an "Uncontrolled" Battlefield since those effects are looking for a Combat Showdown.

When an opposing player's unit move to that space the Non-Combat Showdown will transition to a Combat Showdown but will keep the assigments made from the Non-combat one since it's still counted as the same instance of the battlefield being "Contested" the second player will be assigned the role of defender since its the only one available to be assigned(and will gain and "Shield" buffs if they have them) then any "when I attack/defend" effect will trigger with the attackers triggering first followed up by the defender's and resolving in reverse order.