Blower motor turns on before furnace heats up all the way
No, that sounds like it's running correctly. If you want to adjust the timing, you can install an On Delay Timer on your circulation fan. You can use the ICM251 Fan Blower Control - Dual On/Off Delay Timer. It has an Adjustable Time Delay, and a 20 amp 120 volt relay built in. The On delay lets air reach proper level prior to energizing fan, and the off delay purges ducts of residual air to increase efficiency.