It's not too complicated really. I posted about this a few pages ago. Basically there is an option bonus each year that is essentially a new signing bonus. That bonus is pro-rated for 5 years each time it is paid out. So each year that passes, you are tacking on 1/5th of each option bonus that you have paid him so far.
Philly has already paid him some signing bonuses and option bonuses, and when he is traded, all of the leftover money they still owe him will be due. If they traded him before June 1st, it would have all accelerated onto this year's cap. By trading him after June 1st, they only have to pay him what they would have already owed him this year, and the rest of the balance is deferred onto next year's cap.
For New England, they only need to worry about the option bonuses that are due this year and going forward. So, they are paying one option bonus this year in real cash but only paying 1/5th of it on the cap, which is why the cap charge is so low. Next year they will again pay another option bonus in real cash, but only 1/5th of it on the cap, plus another 1/5th of the prior year's option bonus. In year 3, again, another bonus paid in real cash, but 1/5th hits the cap, plus 1/5th of the prior year, and 1/5th of the one from two years ago, etc...
Eventually the contract ends and the balances of each option bonus that are still left accelerate to become due. Each individual bonus will have varying balances remaining which add up to that larger cap charge.
I have proposed that they likely would cut or trade him in the last year of the deal to avoid his last option bonus and also end up with a smaller dead money charge (around $45M instead of $55M). He will be 32 years old by then so likely slowing down. In the event they want to keep him around, they could instead extend him a couple of years to add years to the deal and keep spreading out the option bonus pro-rations and kicking the big dead money hit down the road. Either option is doable depending on preference 3-4 years from now.