The Campaign Arbiter gives you the following information about who gets what crystal:
The young Elvaan wearin' the red hat is a blacksmith = Fire Crystal
The adorable little Tarutaru with the blonde braids is laying plaster = Ice Crystal
The Hume lady is a stonemason, and a darn good one = Wind Crystal
That old coot of an Elvaan with the huge axe strapped across his back is a carpenter = Earth Crystal
May not look it, but the Mithra with the black kerchief wrapped 'round her noggin is an architect = Lightning Crystal
That sprat of a Tarutaru wearin' the blue getup's a handy lil' plumber = Water Crystal
The good-looking fella in all white does scaffoldin'. Young Hume lad = Light Crystal
The lady Elvaan's a painter. Handles a brush like nobody I never seen = Dark Crystal
You can determine the crystal that they need depending on what they are wearing, along with their race and gender.
Multiple NPC's will show up, so there is no correct order to give out the crystals, just give out the ones that need to go with who is shown.
If you take too long, the NPC will leave. The time you have to make your selections is much shorter than in the first two Ops, so you need to be very fast to succeed.
Successfully completing this mission will increase the Fortification's Max HP up to a maximum level of 300.
Make sure the NPC's come to a complete stop before trying to give them a crystal. Pressing too early will cause it to miss, and with such a long delay before you can choose another crystal, it can be instant failure.
Allied strongholds must be fortified to withstand assault by Beastman siege turrets. Travel to one of our nation's areas and oversee the construction effort.