I don't know what type of HID conversion kit you got? I bought mine from eBay.
http://cgi.ebay.com/ebaymotors/ws/eBayISAPI.dll?ViewItem&item=390032291858&viewitem= &sspagename=STRK%3AMEWNX%3AIT
If you follow the link you will see a diagram. You have to have a relay. Otherwise, it might void your car warranty if you had electrical issue.
The relay will get a signal from one of headlights socket. The power feeds directly from a battery. Hi and lo are controlled by Bi-Xenon Controller.
I don't have any problem with my HID yet. It has been 3 months on the FIT. However, I have HID on my 2007 Civic Si for almost 3 years now with no problem.
Please let me know if you need further assistant.