I'm not certain but the way it reads is that OP used the LED spots in addition to the OEM 4.5's - so plug n play connector would be moot
(if he substituted them you would have to believe he would just have used the wires that powered the original lamps, regardless of their connector type)
Current it not leaking INTO the 5.75, it's leaking OUT and this is what is feeding the aux lamps in his case (except when he turns off the switch which breaks the circuit path)
You would not notice this since you wired into the OEM aux lamp connectors, which would be disconnected from the headlight when the relay turns off.
Besides, these bulbs are not necessarily the same anyway and fact yours has a fan would probably discharge whatever residual stored voltage may be present at turn-off.
Regardless, the way you have it connected is correct and when OP rewires his to the correct location, it will no longer exhibit the problem.