hmm, i think the concept of "speed" is being confused here, and possibly not accurate in the manual.
there are 2 types of AE - Position and Speed.
Position monitors the % travel of the pedal only. so if OFF value is 5%, if it's under 5, it's off, and if it's over - even just at 6% - it's on.
sometimes people park a pedal in the middle of a Wah range as an effect. but if your pedal is loose it may creep down and eventually go Heel Down. if set to Position AE, once it passes 5%, the Wah would turn off. people may not want this, as it accidentally became lower and lower.
to combat this, Speed type AE was made so in addition to the 5%, the pedal has to move "swiftly" to register the on or off. in the creeping pedal situation, because it moved slowly down, the Wah wouldn't turn off at all since it didn't move "swiftly" to indicate intent of moving it. (the Wah would also change tone, but it wouldn't turn off.)
in addition to that, there are 3 "rate" settings, i'll call them. Fast, Medium, and Slow. these determine how quickly the effect turns off once you hit that threshold. with Fast, when you get below 5%, it almost immediately turns the wah off. with slow, i think you have about 1 second or so where the wah is still on, and then it turns off if you stay under 5%.
that's all those "rate" settings do. i'm pretty sure that when set to Slow, the wah doesn't take 1 second to turn on.
so all that said, i don't understand how you could have a "slow" engage. which means if you set the Rate to Slow, the engage should be immediate, and the disengage should be slow. again, i've never had the Wah turn on "slowly" only quickly ever.
can you record some audio showing this?