Fire-Control Team

If a ship equipped with Fire-Control Team resolves the critical effects of both Assault Proton Torpedoes, and XX-9 Turbolasers, the damage card dealt by Assault Proton Torpedoes would be the “first” faceup damage card dealt and if any damage is then also dealt to the defending ship’s hull, it would suffer its “second” faceup damage card as XX-9 Turbolaser applies its effect. Only two critical damage cards would be dealt faceup in total.

Reference

If a ship equipped with Fire-Control Team resolves both the XX-9 Turbolasers critical effect and the standard critical effect, only the first 2 damage cards are dealt face up.

If a ship with this card equipped resolves both the Assault Proton Torpedoes critical effect and the standard critical effect, only the damage card dealt by resolving Assault Proton Torpedoes is dealt face up.

After the “Spend defense token” step and in the “Resolve Damage” step, the attacker may exhaust this card to resolve another critical effect, but cannot choose to resolve the same critical effect. IE, cannot choose to resolve Assault Proton Torpedoes twice. But could choose to resolve Assault Concussion Missiles, and the standard critical effect.

The player chooses in which order to resolve the critical effects.

Upgrade cards or Objectives that grant access to non standard critical effects can only resolve their critical effects from the appropriate colored dice in the attack pool with the critical icon showing.

Upgrade cards or Objectives sharing the same color of die can both trigger from one critical icon showing when exhausting Fire Control Team, multiple critical icons of the same color die are not needed.

As per the FAQ, in regards to any combination of the standard critical effect/XX-9 Turbolasers or XX-9 Turbolasers/Assault Proton Torpedoes.

In the case of XX-9/Standard critical, XX-9 has the first two damage cards dealt face up, meaning the standard critical effect is resolved when the first damage card is dealt face up.

In the case of XX-9/ Assault Proton Torpedoes, the Assault Proton Torpedoes faceup damage card counts as the first face up damage. A second damage card will also be face up if further damage cards are drawn during that attack.

And in the case of the standard critical effect and Assault Proton Torpedoes, resolving both critical effects fulfills the requirements of both, in that the first damage done to a ships hull, is a face up damage card, meaning a 2nd face up damage card would not be drawn.