How Accurate Are Kits Of Ovulation Tests?

Hi, I recenlty took a five day dose of clomid for ovulation issues. on day three after finishing the cycle of clomid I took an ovulation test. It showed positive for LH surge. The day I tested was on day 12 & I took the clomid on days 5-9. I have read that this would be an accurate positive as I waited until day three after the cycle of clomid, & the insert witht he test also stated that it isn't affected by clomiphene citrate. Do you think this was an actual LH surge & thus a precursor to impending ovulation?