The NBA is weird, the trade wasn't "official" so Boston picked for New Jersey. Like in the NFL when a team trades up to get someone, that is what NJ did I believe but it wasn't "official" so it was still Boston's pick technically... we never had rights to him I believe.
Not sure what you mean by "official".
My understanding is that there are a lot of restriction against trading first round picks. For example, you cannot trade 1st round picks in consecutive seasons. You also cannot trade first round picks on the day of the draft.
On the other hand, you can trade the rights to players. So if teams want to trade picks on draft they, they have to pick in their own spots and then trade the rights to the drafted players.
So the draft picks were not traded. The rights to the drafted players were traded.