i am not familiar with the kit by any means but am familiar with wiring, if your fan runs with the thermoswitch unplugged then its getting power and ground from somewhere directly to fan without going through switch, recheck your wiring, if this kit is a plug and play kit i have seen other premade kits (trailer light kits, car accessory kits etc , not your fan kit) come with wires backward in the harness, id start by checking power and ground at wherever the fan harness attaches to your stock harness... a lot of diffenet scenarios could happen if one wire gets switched...
when i installed my homeade fan kit i was going to take power from headlight circuit, acidently tapped into the wrong red wire and when i actuated the fan switch the starter also tried cranking and the fans turned on at same time, i resspliced to the other red wire that was actaully for the headlight and not the e-start button and was good to go lol, didnt take long to find that mistake, glad it was in neutral 8O
good luck