Why would there ever be a circumstance when the current elected president of the district is not the voting DPA member?
The rationale has to do both with the fact while some presidents are elected at spring meetings they don't take office until July 1 and also in a desire to have greater continuity in the Districts President's Association (DPA). Many (if not most) outgoing district presidents who are not officers of the DPA or on a key committee of the DPA (e.g. Annual Program Fund (APF) Liaison) designate their newly elected president to represent them at the General Assembly (GA) meeting or they both attend the GA meeting so that continuity in leadership can be established quickly and before the big November meeting.
Districts vary as much as congregations. The DPA membership policy was intended to be a leveling one.