How to Sync Booster Fan with Furnace Fan
Using a 24v/110v relay (installed in the booster fan's junction box) run 2-conductor T-stat wire back to your furnace.  hook 1 conductor to ground, and hook the other conductor to your T-stat's fan wire (usually green, but whatever wire is connected to the "G" terminal on your T-stat).  On the 110v side, break the black wire to the fan and connect leads to the relay.  That's it.  Alternatively, you can use a pressure switch, but they cost more and you'll have to run power (110v, 14/2) from the pressure switch (which should be located in the supply plenum just downstream of the cooling coils) to the booster fan.