SWTOR Community Manager Eric Musco explained how to unlock Corso and Risha (Smuggler) and Andronikos’s (Inquisitor) the missions for recruiting these companions during the Knights of the Eternal Throne storyline.
First, you must be a Smuggler to be able to unlock the missions for Risha and Corso or be a Sith Inquisitor to get the mission for Andronikos. Also you need to have completed the Knights of the Eternal Throne story expansion. The reason for that is because the missions for these 3 companions take place after the events from the 9 chapters of KOTET.
Once you cover the requirements, a new Alliance Mission Alert will appear for you. If it doesn’t, you may report it as a bug to be listed with the rest of the Known Issues here.
The Dev team is fully aware of the popular demand that these companions be made available to be acquired by other classes via the Companion Locator Terminal on Odessen. However, this is no simple task, as Musco explained it in a Forum post. This is something that may happen, but perhaps in the future. A feature like that cannot be offered quickly to the players.