All of my spotting occurred after getting a positive test too. Mine was about a week after my expected period and Dr said it was most likely due to the placenta implanting in uterus
I had a similar experience. When I began spotting, I thought it was my period. My periods were irregular. Prior to, my tests were always negative. Post, spotting, my line was faint. I'd take weekly tests and the line progressively darkened. At that point I went to my OBGYN who confirmed my pregnancy.
Id say the tests are positive.