When I worked on the Kodak Instant Photography system ('76 to '83), I used to make prints on the Kodak film units with my enlarger. After exposure, I would insert the exposed film back in a pack - put the film pack in a camera - and then eject it from the pack using the camera (with it's lens covered).

BTW, the Fuji Instax film is basically the sames as the Kodak Instant Film. Fuji had licensed the technology from Kodak and Polaroid sued Kodak but let Fuji continue to make the film for use out side the US.