A319 Captain reported encountering wake turbulence in trail of another Airbus while descending on the arrival.

Narrative

While on the GESNR1 RNAV STAR; our aircraft incurred jet wash-induced uncommanded rolls left and right near ZOEEE. Another aircraft on same arrival was only 4 miles in front of us and winds were directly parallel to our heading. Immediately after incurring expected jet wash conditions I disconnected the autopilot and chose a heading right of course to escape the uncommanded rolls. We immediately informed ATC that we required a deviation due to flight conditions. Initially they said that we were unable to deviate. We repeated that this was not something that can be avoided and required immediate deviation due to the nature of jet wash conditions. As a result of this situation we did go off course and ATC instructed us just to re-join as soon as possible. Additionally; ATC could not understand why we were in jet wash conditions because the aircraft we were following was another Airbus. As I recall; my First Officer told ATC that we were in those conditions whether he understood it or not and we had to take actions. Rolling around in jet wash at 7;000 ft. was unacceptable and only being 4 miles behind another Airbus with direct winds in face made this condition 'expected'.