Hmm, in my eyes is because MC was really lacking in the memory aspect, he was almost the same as he was on level 1 (difference being memory echo), so the training really gave him a huge jump in power.
The thing is that Mc wasn't really just sleeping, he jumped to the dream world with help of Shen's powers and his moms training. We can see that the eye has a connection with this place providing him infinite energy or something like that, so we know it really exist this Dream World and can affect the real one.
The power he gains is for his memory powers, not his shapeshifting, but as a lv3, every ounce of power he gets directly affects his physical strength too, that's why he's stronger when he wakes up.