Starting from cold e.g. early morning or after standing for a couple of hours, the starter motor carries on running for 2 or 3 seconds after the engine has started.
A new starter motor was fitted in April this year and the battery is about 2 years old.
Running Rough, Starting & Power Loss
the starter motor should stop when you release key cutting power to starter get your ignition switch checked
Possibly the mechanical lock sticking causing the switch to stay on or a faulty switch as there plastic and not very good ,but more likley just the mechanical lock requires lubricated.
If you can move your ignition key back ever so slightly when the fault happens it should stop the starter running and prove that the fault lies with the ignition.