Furnace blower comes on full time when the thermostat is set to Auto
Something here isn't adding up. Your post states that when you place the fan selector to auto, the fan immediately turns on. The fan should be running before you select auto. The fan selector switch has two positions on and auto. On - closes the connection from R to G bringing on the fan. Auto - does nothing at the thermostat and the furnace will bring on the fan as required.

So from your post I can deduce there is potentially a problem with the thermostat. The simplest way to diagnose where the problem is to 


Unmount the thermostat, check the state of the furnace. It should be doing nothing.
Mark down the wire locations. Jumper R to G. The fan should come on.
Jumper R to W. The burner should fire and the fan should energize within about 2 minutes.


A thermostat is little more than a set of manual switches that operate based on temperature. If the instructions above provide different results then outlined my next guess would be that the board was somehow wired incorrectly.

The board could have a continuous fan selected by dip switches but it wouldn't shut off when setting the thermostat to off. So again it looks like a faulty thermostat. The only thing I can think of that wouldn't be the thermostat is a continuous fan speed set high and the cooling fan speed (G terminal) set so low that it is not noticeable.

If the stat checks out, more information is required to determine the problem.