According to this NMC don't have to follow a player to a new team:
What is a No-Move Clause (NMC)? A No-Move Clause (NMC) can be added to a player's contract in the years after they are eligible for Group 3 Unrestricted Free Agency (7 Accrued seasons or 27 years of age), and has the following properties: Player cannot be traded without his consent (however, the clause can specify a modified no-trade clause that limits the NTC to a certain number of teams) Player cannot be placed on waivers without his consent Player cannot be assigned to the minors without his consent Player is not exempt from a buyout or contract termination The clause can travel with the player even if he consents to being traded or is claimed on waivers This requires that the acquiring team sign an addendum to the contract ensuring that the clause does in fact travel with the player (written by the player's agent) If the acquiring team refuses to sign the addendum, and the player waives his clause anyway, at that point the clause may be nullified If the player is traded before the clause takes effect, the acquiring team can opt to void the clause