I used the kiosk by Philharmagic on two different days when we were there a couple of weeks ago. Both times it was probably around 9:30. (We'd hit rope drop, ride a thing or two, then get in line.) Anyway, the whole process from line to having FP's in place took maybe 10 minutes. Later in the day, there was more of a line there.
At AK, we hit rope drop and headed for the Safari first thing. When we got there, Safari was a walk-on so I went ahead and reserved my FP right there at the kiosk before riding - no line.
At DHS, we hit rope drop and went to TSMM first. Rode that, then got the FP at the kiosk right there. Again, no wait.
At Epcot, rope drop, rode Soarin', then got FP's outside The Land where there were several CM's with IPads - no wait.