It takes the pedal about 1-2 seconds to go into bypass mode after you hit the on-off button. Is my pedal broken?
No, your pedal is not broken. This happens due to the ramp mode /"hi-speed enable " feature of the pedal that is activated on all of the 3 standard settings.
If you bypass the pedal the Modulation speed will ramp down to zero according to the attack and release times of the setting/TonePrint. if you want an instant bypass where the signal is cut instead of the Modulation fading out (as a real Leslie would do), you have to create a TonePrint with the TonePrint Editor or modify an existing template: set Hi Speed Enable parameter to "off" and Attack and Release times to the minimum setting.
Please note: This will only effect the TonePrint setting. Vibrato and Chorus will remain as set in the factory.