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Do pink horrors get to roll a spell immediately when they hit the table? OR bc they weren't part of the army at the start of the game, they just get flickering fire?

The rules for Conjuration psychic powers are clear that if the summoned unit is a psyker they immediately generate psychic powers.

This however only applies to units summoned by Conjuration powers. there isn't anything letting a psyker generating powers if made through other means (such as the portalglyph or the Warp Storm)