The Alter of Fecundity is where you make the blanks/base items. There are a few recipes in there as well for things like Radiant Forcefield Clickies.
The alters in the raid are where you combine the base mats into gems / focuses / essences.
Those gems, focuses and essences are then combined to create the augments that will go into the LGS base item blank.
Most of those augments are also created in the alters within the raid, but as mentioned, some can be created at the alter of fecundity, but the main effect augments are all done inside the raid.
Tier 1 gems, focuses, essences, and augments are crafted at the Alter of Invasion at the end of phase 1 of the raid.
Tier 2 gems, focuses, essences, and augments are crafted at the Alter of Subjugation at the end of phase 3 of the raid.
Tier 3 gems, focuses, essences, and augments are crafted at the Alter of Devastation at the end of the entire raid.
The other alters that are in the airship are for heroic greensteel crafting.
So yeah, base item blanks are made outside the riad at the alter of fecundity, most of the actual crafting though is done inside the raid itself.