Oh, another good question. The AI reinforcements are done based on when an internal counter reaches 2400, not based on any actual timers. Each of the two AIs has their own wave and reinforcement timers and counters, and they each have their own reinforcement events, so the other thing to remember is that everything is essentially 2X in aggregate between the two, although there is no guarantee that the reinforcements and waves of the two AIs will happen at all in conjunction with one another.
So, for reinforcement timing, that's based on a counter that must reach to 2400. The counter increases once per second as follows: AIDifficulty + Random( 2, 4 ). So mostly it increases on a fixed amount per AI difficulty level, but there is a small random component in there, too (the lower bound is inclusive, the upper is exclusive, so you really can only have the values 2 and 3 from that random there). So for a difficulty 7 AI, you will get reinforcement events somewhere between every 266.67 and 240 seconds (assuming no handicap).
When a reinforcement event occurs, it reinforces 1/2 the number of planets that the human players control, up to a cap of 15. It can't get less than 1 planet. On difficulty 8 it gets 1 extra planet always (even above the cap of 15, making the cap 16 there), and on 9 it gets an extra 2 planets above the norm, and on 10 it gets an extra 4 planets above the norm.
Also of note is that if the AI has a handicap, its cap of 2400 is reduced by whatever the handicap is * the total. For example, with a handicap of 30%, the actual cap is ( 2400 - ( 2400 * .3 ) ) = 1680. The cap can never be driven below 800.