Geistblast

If an alternative cost was paid for the spell, such as its madness cost or surge cost, the same alternative cost is considered to have been paid for the copy.

If the spell being copied has an X whose value was determined as it was cast (like Avacyn's Judgment's madness cost has), the copy will have the same value of X.

When Geistblast's ability resolves, it creates a copy of the instant or sorcery spell. The copy is created on the stack, so it's not "cast." Abilities that trigger when a player casts a spell won't trigger. The copy will then resolve like a normal spell, before the original spell resolves but after players get a chance to cast spells and activate abilities.