The two fans in the front stops when I turn the ignition off, should they do that?
And when I have the engine running or driving, they work exactly as they should.

1992 3,8L

Yes they are operating as intended.

Okej i trust you.

But on some other cars with an electric fans, they start at any time (as long as the engine is hot) to cool it, even if it not running.

Since the engine/waterpump is not operating those fans can cool the radiator at best, having no effect on the engine temperature since the cooler water is not circulating through it without an operational waterpump.

On the 3800 versions the Fans are PCM controlled... They are not switch actuated... The PCM actually turns on the fan relays to operate the fans..:)