Their design is usually that of an afocal Galilean telescope that alters the width of the entering beam of light without affecting the divergence of the beam, so they can change the effective focal length 1 to 3 times without increasing focal ratio.
The down side to teleside converters is they will vignette the image on the wide angle setting if used on a zoom lens.
[3] Minimum focal length without vignetting will increase inline with higher power of the teleside converter.
The other concern is minimum working distance, so the teleside converter cannot be used below minimum working distance and it depends on both the camera and the teleside converter being used.
Since teleside converters are afocal they can be mounted universally on almost any camera lens via adapter rings designed to fit the filter ring of the camera's primary lens.