No one has to join your game.
Simply load up any Classic Prison (there are 7) (Transport Prisons do not count), then press
, then go to right side of screen and change game to public. Back out to the game and your achievement will unlock.
Classic Prisons are:
Centre Perks 2.0
Rattlesnake Springs
K.A.P.O.W. Camp
H.M.P. Offshore
Fort Tundra
Area 17
USS Anamoly