When I change from STOP to RUN the control output overshoot becomes large. What can I do about that? There is no problem with PID tuning.

Try the PV tracking function (PVT=ON). This function is useful for preventing sudden changes in the PV value. When operation starts, the PVT starts by matching SP to PV, and then uses an SP slope function (TMU, UPR, DNR) to gradually return SP to the originally set value.