Cid has a different type of amnesia then everyone else does. Everyone else the WoL runs into in 2.0 have just forgotten the WoL and the specifics of what happened at Cartenau. Cid has forgotten literally everything. When you meet him in 2.0 he doesn't remember that he's Cid or that he's an engineer or that he was originally from Garlemald. It takes the WoL's Echo to fix that.

If you are on a character from 1.0, everyone else somehow remembers you after Ultima Weapon is defeated.