You can only activate pink ONCE BETWEEN TURNS powers on other players' turns, not on your own turn.

This is supported by the following rule:

• "ONCE BETWEEN TURNS (pink): These powers may be triggered on opponents’ turns. You can only use a pink power once between each of your own turns (if an opponent triggers it)."
  (Page 10)

This means:

• Pink powers are not activated during your own turn, even if the condition is met.
• They are only triggered by actions taken by opponents during their turns.

Source: page 10.

Source: Core Rulebook (pp. 1, 10, 4, 7, 8)