I think In the actual built circuit shown as picture posted, the star contactor is connected to the thermal overload terminal from motor side, which is more safety may be, not from delta contactor side as shown in power circuit diagram.
thanks for your schematics
i made the start delta control circuit in fluid-sim, and i releized that it repeat the cycle when you press the start button again, and as solution i suggested to energize the main contact first.
Star Delta Starter Control Circuit Diagram Pdf Download