Probably because the OEM springs were allowing the rearend to squat more when you nailed the throttle. That=more weight transfer to the rear=more traction. Stiffer springs, if that is what you got, will not allow that as much. This is why drag spring rates are pretty soft.
But yes the new tires should help out a lot, so will some good LCAs.
2000 Mustang GT Steeda #0048 34k miles. 99 Cobra 4V swapped, FTBR IRS swapped, exhaust, tuned by James Gordon.
Just because I give you advice, doesn't mean I know more than you. Its just means I've done more stupid ****.