Motor starting requires lots of reactive power from power supply. Due to this reason, there are large voltage dips when motor starting, if reactive power supply is insufficient. I guess that your capacitor would supply reactive power to compensate required reactive power demand when motor starting. After start-up, it help improve power factor.
I am not sure which kinds of trips arose, but I guess that magnet contactor (MC) in motor starter could be released due to large voltage dips when motor starting although 375kW motor would be started. It is one of possible case, if MC is a inferior unit. If my assumption is correct, please check and test MC first.
If 375kW motor failed to start-up and its starting behavior trips other equipment, your present system does not provide the required reactive power when motor starting.
Therefore, I suggest you to increase opearating voltage of in-plant generator within its permissible operating region to supply more reactive power to your system for motor starting.