There is an option on the cutscene component inspector called “Default Stop Mode”. This determines whether or not the cutscene will be rewinded, skipped to the end, or none of those (hold) when the cutscene stops, which can also be the result of calling Stop() manually.
What option do you have selected there for your cutscenes?
You can also force a specific StopMode when calling cutscene.Stop() by providing a StopMode parameter likeso:
cutscene.Stop(Cutscene.StopMode.Hold);
Can you please try setting this option to Hold, or alternatively call Stop with the parameter as shown above?