You only get many mines during the laser phase when your players with the mine are /stucking or running into the laser. Have them move to a different corner, out of the group, and have your healers keep them alive as long as possible. That way, you'll only get two mines and not four or more.
The boss always starts the laser phase at 3:30 min after he appears, at which point he should have around 30% of his HP left, but depending on your DPS this can vary of course. However, you can time the jump, it is not random.
Two slight corrections/clarifications.
1) Although more mines may go out during laser phase if people deliberately suicide this isn't guaranteed. We were having our people suicide and on the kill still only had two go out. That being said, knowing only two will go out instead of maybe two and maybe more is of course preferable. We were willing to accept the higher losses in 16 man since with one shadow tank and 2 scoundrel healers and 10 DPS, we were sure we'd have enough bodies left at the end to actually kill.
2) While there is a hard time limit on when he jumps, I believe there is also a % flag. He always jumps soon after the third set of adds after he appears (4th set if you count the opening set of mobs before the boss himself shows up). However, we found that if we left melee on the boss at all times and let ranged deal with the adds, then we could push him to sub 20% before a third set of adds pops and he would jump before the third set popped. Since the adds always appear on a set timer, I presume that the mechanic is that he goes immune and jumps at a certain % OR at a certain time (3:30 from spawn) whichever comes first. I personally recommend burning inspirations after the first set of popped adds (second set total counting the initial group) and then pushing again hard after the second popped set (third set overall), while leaving melee on the boss if possible, and then you skip the third set of adds entirely. Having him come down from unified beam with only 10-15% health left is quite nice.