When to turn your alien power face up?
By default, alien powers are revealed after everyone has one. The rulebook does not make this clear up front, but it must be true since the other option you mention is in the Variants section on p14:

Hidden Powers
In this variant, players leave their alien sheets facedown after
selecting them at the start of the game. While a player’s alien
sheet remains facedown, its power cannot be used. A player
may turn his or her alien sheet faceup at any time in order to
use it. Once turned faceup, the player’s alien sheet remains
faceup for the rest of the game.