It is a more subtle control, and yes, much like saturation due to magnetic tape, it does depend on your input level. Since it only applies to the repeats try listening with the both delays set to no delay and the mix all the way wet. Turn the saturation knob and you'll hear slight compression in the lower knob ranges, to more compression (especially on attack portion) in the mid to upper mid range of the knob, and then some slight distortion with the knob all the way up. Combine these sounds with the filter knob (a low pass filter) to get some retro repeats.
I would also try using a gain boosting pedal before the TF to get more level, and be careful with "True Bypass" pedals and/or really long cables from passive guitars. These situations cause most of your signal to be loaded down at the pickups resulting in a significant gain loss (especially in the high freqs).
