It took a few weeks for us. Our dietician told us to give it 3 weeks as it takes time for the old milk to leave their system. My little boy was on Nutramigen for all of about 3 days before being moved on to Neocate. Nutramigen didn't agree with him and they think the reason was that it still contains cows milk protein, albeit broken down into tiny particles. I guess it depends on the extremity of the intolerance/allergy but we noticed a definite improvement once he was on the complete dairy free milk. He's been on it for a few months now and for the past 2 weeks or so, his reflux has pretty much disappeared- he's now 4 months old.
Be patient as the improvement may not be immediate but hopefully you'll see a change within a few weeks.