Lay off the assessment books. He is already having tuition for all subjects which means he is already doing more work then assigned by the school. I would actually say lay off tuition of he is still giving average of above average results but that depends on your expectations of him I guess.
It is not uncommon for kids moving from P1&2 to P3 to experience some drop in their grades. If his foundation at P1 & 2 is sound, what can be done is to get him to understand that questions and sums are no longer that straight forward and simple. DD too was in P2 mode when doing her first tests, she glanced at the questions and made assumptions without reading the questions properly, which lead to a lower then average score.
I think most importantly, what your son needs now is encouragement, not more work.
C