If your diesel engine continues to run for a minute or so after you shut the ignition off then it's likely that some residual diesel fuel is still in the engine where it's compressed.
Diesels ignite the fuel through compression to create the explosion in the cylinders unlike the gasoline engines that use spark to ignite the fuel.
So another possibility is that the fuel pump is not shutting off due to a bad fuel pump relay or the fuel injectors along with the fuel pump is not being turned off.
I had a diesel truck that used to run for 2 minutes after I shut it down and it turns out it was just because it was getting too much fuel into the engine and it took a bit longer for the engine to shut down after turning it off.
I sold the truck and the person who bought it fixed the issue.
So you might want to take the vehicle to a diesel mechanic who knows diesel engines and how to fix them because the engine should usually shut off right away after you turn the key to the off position.