Actually the modulus needs to divide the number of possible output of rand(), which is by definition (MAX_RAND - MIN_RAND + 1), if you want to have a uniform distribution (assuming your rand function has a uniform distribution).

In the specific case of mt_rand, MIN_RAND is 0 by default, then the modulus needs to divide (MAX_RAND + 1).

In the general case, there's no rule in any uniform continuous implementation of rand such as (modulus + 1) needs to divide a specific number.