With the fuel injection being electronically controlled, as soon as the key is turned off, it should kill the injectors. The questions asked by Koalar are to determine if the key switch is still 'on', or if the ECU or a relay is keeping the connection.
How does the ignition switch feel in use? Is it a nice firm action between clicks? Does it stay firmly at each position, or is it loose? When this issue occurs, have you tried wriggling the key a little to see if that kills the engine?
Do you have lots of 'stuff' dangling from the ignition key? Many people do, and the weight can cause rapid wear to the lock. Ideally, there should be the ignition key, and a keyring/fob only. Adding one key such as front door, or a token for the supermarket trolley should be OK, but avoid adding more.