Containment Priest vs. Mutavault/Inkmoth Nexus

[Paranoid__Android]

I have a Containment Priest on the battlefield. Opponent can't activate any manlands like Mutavault or Blink/Inkmoth Nexus, or can he?

[Koby]

I have a Containment Priest on the battlefield. Opponent can't activate any manlands like Mutavault or Blink/Inkmoth Nexus, or can he?

Containment Priest
Creature — Human Cleric 2/2, 1W (2)
Flash
If a nontoken creature would enter the battlefield and it wasn't cast, exile it instead.

Mutavault
Land
T: Add {1} to your mana pool.
: Mutavault becomes a 2/2 creature with all creature types until end of turn. It's still a land.

Mutavault is already on the battlefield before you can activate it's second ability.
Containment Priest has no effect on Mutavault and other lands that activate to become creatures.