Just like you said,
total mag attack = mag reinforce * int + mag attack + magical attack, so thats why a pure int hits so much higher with nukes than a hybrid int or a pure str ... same goes for str.
Also the defence reinforcements work this way, phy def = phy reinforce*str + phy def
As your lvl gets higher you get more and more str and int and the reinforcements will become increasingly important.
Example is this 98+7 Staff:
The mag reinforcement goes up to 575.9%, so thats 5.759 * int (which will be a lot for a pure int wizzard at this lvl) + the mag attack of the staff, this gives the total magical attack that you see in the character window
