CHECK THIS OUT!
This is a method of color screenprinting shirts called CMYK printing, which uses Cyan, Magenta, Yellow, and blacK to product a full-color image, just like a color 2D printer would.
In order to ensure proper alignment of each layer for each Tee shirt, precise coupling of some kind must be used. If you look at the bottom right, it seems some kind of endstop is used to ensure each screen is located properly in the horizontal direction, and the rood itself butts up against the metal frame to align the vertial direction and prevent rotations. While this may not exactly be micron repeatability, this certainly seems good enough for this application! Perhaps I should make a Kinematic Screen Printing Coupling? Maybe in the future!
Here's a video of a photographic image recreated by this process. This time, a machine is used with four stations and four tee shirt holders that move from station to station, where each station only puts down one color. I imagine some kind of final alignment features are used in order to get each station to be repeatably applied to each tee shirt.