I should have been more clear. If I were his trainer, ideally, I would want to follow 5/3/1 or something like that with barbells and dumbbells both being involved if he is a beginner. For most people, if the weights go up muscle usually follows. I myself like training my clients for strength and might get to aggressive loading up the bar with some of my clients too fast, so I am constantly having to stop myself from adding too much weight too quickly with some.
Any program that has some progression should work. There is just some that are better than others. I will say i dont like his program of only dumbbells. But if the trainer does not know barbell training or is not comfortable with them he is not gonna use them.
Dumbbells offer more of an aesthetic improvements for me than barbell work. Is he using 50+ reps per set with just dumbbell work?