Why is my furnace blower coming on so early in the ignition process?
Most furnaces use a preset, adjustable, time delay circuit to control the start of the blower motor. Some higher end models may use a temperature sensor to determine when the blower should come on, but this is a less common setup. It's possible that something in the furnace is broken and/or configured incorrectly, but it's more likely that the thermostat has been installed incorrectly. 

A thermostat in its most basic form, is simply one or more thermally activated switches.  In the olden days, it was likely a mercury switch, that only controlled a heater.  Most more modern thermostats control heat, A/C, and the blower fan.  In your case; since you're having trouble with the fan, we'll focus mostly on the fan settings.  

A typical thermostat will only have two settings for the fan, ON, or AUTO.  In the ON position, the fan will run continuously.  In the AUTO position, control of the fan is handled by the furnace instead of the thermostat.  Since your fan does not run continuously, I'll assume you have the fan control on the thermostat set to AUTO.

If you accidentally connected the FAN wire to the HEAT terminal and/or the HEAT wire, every time the thermostat called for heat the fan would immediately turn on.  Since this is the easiest, cheapest fix. I'd start by making sure the thermostat is wired properly.