Electric coolant fan wiring relay

[Highsteel]

I got my fan installed and wired up according to the kit manufacturer specs I got from the parts store. All went well, temp stayed normal, until I went to turn the truck off. Now there is like a 2 second delay from the time I turn the key off til the engine turns off. Its not dieseling, it just stays running for a bit, then shuts down.
Is this because there is no relay? I have a relay that came with the (used) fan but I wasn't sure where in the circuit to put it.

Jerry