It's illegal to have fogs that come up with the high beams. Those instructions were written in China I bet. Hook it up to the low beams, or if you really want to use it with high, hook it up to the driving light (what's is illegal as well but it's up to you). Or even better, tap it into your OEM fogs WJ has 2 bulbs, one for high and one for low, so there shouldn't be a problem to figure out which one is which as long as you identify the ground wire(use multimiter to ring it for continuity to the ground).
No need to cut the wire eather, tap it right by the headlight using this tipe of connector.