Could this be the
long-tail slip effect happening? In a turn, the airflow is curved but the fuselage is straight, so the airflow can be aligned (zero slip, or beta, angle) either at the tail or at the CG (or wherever the IMU is installed) but not both - you have to choose one or the other. So, if the inclinometer shows centered, that means there is a slip angle at the tail. Or, conversely, if there is no slip at the tail, there
is slip at the CG (therefore side force, therefore off-center inclinometer). Usually negligible, but could show up in a long enough airplane in a tight-enough turn. And a basic yaw damper cancels yaw
rates but not steady-state conditions of off-center yaw, so it allows this condition to persist.