It sounds like I-term windup on a quad that has mismatched power on the arms.
One or more of your motors/ESCs/props is stronger than one or more of you motors/ESCs/props.
I assume that all your motors, ESCs, and props(L/R) are identical and that ESCs all have the same firmware (and settings), if not, make them the same (or read below).
I would start by calibrating all ESCs at the same time to make sure the top ends are set correctly as that would cause what you mention.
https://librepilot.atlassian.net/wiki/display/LPDOC/ESC+Calibration
You can (/ should be able to) reduce your stronger motors to the same strength as your weakest motor by reducing the Max for the stronger motors on the Output page. You may have to reduce it a fairly large amount to get it to actually reduce because of deadband at the top end. Refer to previous link about removing top end deadband too. Trial and error or some sort of thrust measurement device... I would guess that your back right motor is the strongest. I bet you can tell by (CAREFULLY) running up one motor at a time with the Output page "Test Outputs" option. You can't always go by RPM though (like if it is a prop difference).
Thanks for the advice. While testing out my quad with ASWA enabled and experiencing the above mentioned issue I crashed and damaged one of my ESCs (Kingkong 260 FPV, super brittle frame, ESCs mounted on bottom of frame, very silly design). Once my new ESC is delivered I'll try calibrating all ESCs with the link you provided.
Since it's an RTF kit all of the motors, ESCs, and props are the same (Kingkong 2204 2300kV motors, Kingkong 12A ESCs, Kingkong 6040 props).
Just to be clear, the quad rolls right and pitches backwards just for a split second. It stabilizes, but not at the same attitude the quad had when I reduced throttle to 0. Would the fact that it just does it for a moment, not continually, still lead you to believe it is mismatched power, or could this be fixed by tuning the i-Term? (I have little experience tuning PIDs. I think the quad feels sloppy, so I used some PIDs someone posted for the same quad which they said flew very well)