Whose valve body and what line pressure are you running? Is the valve body low band apply? Also what is your front band adjustment at, along with second gear ratio lever? Is there any “flare up?” when you shift 1-2 or does it seem to happen firmly? Also, what gear ratio is the trans? Is it stock ratio or does it have a 2.74 low gear in it?
Do you leave with both hands on the steering wheel? Or one on the shifter ready to shift after you leave the starting line. Depending how fast the car wants to come out of 1st gear, could be where the increase in rpm is. So it could be a combination of things and there could be nothing wrong with your trans. In my own experience, I watch the tach and the shift light is there to remind me to shift if I am steering the car because it tried to go left or right off the launch.