Well, I think the fact that NJ is a couple million below the cap makes this a bit of a moot point. That makes it pretty easy for us to do a sign and trade with them, since we do not have to match salaries, as long as the amount of salary they are sending out is enough, that they will not be over the cap by taking on Davis.
So if the C's traded them Davis, signed for $4 million, then NJ could send back someone like Jarvis Hayes (who makes $2 million), and be done with it.
But if they wanted to make a bigger deal (that required NJ to go over the cap), the TPE could come into play. This is because Boston will only be able to count 50% of Davis' outgoing salary, while NJ would need to count 100% of it as incoming salary.
So Boston could send Davis ($4 million X .5= $2 million outgoing salary) and then send Tony Allen ($2.5 million outgoing salary), who would be absorbed by the trade exception. Meaning Boston has $4.5 million in outgoing salary, and can take on up to $5.725 million in salary (125% of 4.5 plus $100,000).
For NJ, they would only be counting Davis' $4 million in their incoming salary for matching purposes. So they can send out $5.1 million in salary (say, Najera, and Boone).