Activating a wonderous item is usually a standard action unless specified differently in the item description. Thus, on the round you activate the boots, you spend a standard to activate them, then still receive an MEA and a partial action (so no full attacks). The first round counts against the 10 round per day limitation. It also takes a standard action to deactivate the haste function in them if you turn them off ahead of time.
Your DM is correct, you are incorrect according to the 3.0 rules. If this will change in 3.5 is yet to be seen, the books are not out yet.