My Small Stone has exhibited this behavior since I bought it new years ago:

When you first plug into it and hit the switch, it takes a second for the effect to kick in. The amount of delay time before the effect kicks in is in direct relation to the setting of the rate knob; the slower the rate, the longer the time it takes to hear the effect. If the rate knob is at noon or past (aproximately), you won’t notice the problem. This behavior is only exhibited the first time you hit the footswitch, all subsequent switching on and off will work as it’s supposed to.

Seems like a capacitor needs to be loaded at the beginning of each session, that’s my guess but I’m a dishwasher not an electrician.

Thanks for any help,
Bill