The Bird Rule (3yrs, same team, unlimited resign) carries over from trades. So since he played for the Suns and his rights were traded (rather than a free-agent signing with the Nets), he's all good. Its just like he's been with the Nets for 3+ years. If you want specifics:
Salary Cap FAQ (extremely well done)
Excerpts from the above site that should help:
22.
How long must a player be with one team before the Larry Bird exception can be used?
Theoretically, a player with Bird rights can be traded right before becoming a free agent and his new team can use the Bird exception to re-sign him. There is no specific tenure requirement with one team. The only rule is that the player can't have been waived or changed teams as a free agent for three years. However, if a team renounces a player (see question number 30 ), they can't use the Bird exception to re-sign him for one year.
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23.
Why a three-year wait before gaining Bird rights?
It closed a salary cap loophole. There used to be no waiting period, but this was abused by Portland with Chris Dudley and Phoenix with Danny Manning. Both teams signed these players to one-year deals at small salaries, and the next year, Bird rights in hand, signed new contracts for far in excess of the cap. The three year rule prevents these types of cap circumventions.
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24.
Does the Larry Bird exception mean that free agents can be signed and not count against the cap?
All salaries count as team salary (against the cap). The Bird exception simply says a team can exceed the cap to sign certain players. The new salary applies toward the team salary just like the salaries of the team's other players. So if a team is over the cap and uses the Bird exception to re-sign its own free agent, it will end up farther over the cap.
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25.
I just saw that a team signed a player for more money than it has under the cap. It was another team's free agent, so the Larry Bird exception wasn't used. What gives?
If one of the other exceptions wasn't used, it may just be the way the deal was reported. Only the first season's salary must fit under the cap, but signings are often reported using the average salary for the entire contract. For example, if a team is $10 million under the cap, they can sign a player to, say, a five-year contract for $10, $11, $12, $13 and $14 million in each of the five seasons. The deal then gets reported as five years averaging $12 million, which is more than the team's available $10 million. But the first year salary is what counts, and it fits perfectly.
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26.
Can a team sign all the free agents it wants (up to the cap limit) and THEN re-sign its own free agents using the Bird exception?
Yes, but there's a restriction. A team's free agents continue to count as team salary (against the salary cap). This charge is called the "free agent amount." So there may not be enough money under the cap to sign another team's free agent, because the team's own free agents are taking up all the cap room.
