I've done my own brakes for years, and they should not feel spongy after the first 5-6 stops. They won't GRIP for a little bit as they bed-in, but they should not be spongy at all. If the pedal sinks and requires pumping, your calipers may be still adjusting out to meet the rotors if he pushed them in excessively far, perhaps in the back, although this is doubtful. Make sure you have brake fluid, perhaps something is amiss.
If the pedal is spongy and springs back but is not firm underfoot as it should be, I'd get him to bleed the brakes for you. Some air may have entered the system when the calipers were hung up during the brake job or something. Not sure exactly how this could have happened as its sealed system, but if there is a spongy pedal, its usually time to bleed the brakes.
Fresh fluid is required every few years anyway, so its good idea regardless.