You are not doing something wrong, it's a "design" problem with Superior Drummer, not being properly developed for live/e-drumming.
There are two common MIDI control methods for cymbal choking: sending a "Note Off"- or sending an "Aftertouch"-command. Note Off defines the end of a sound wave by cutting it off, Aftertouch defines what sound to play after a key (or trigger) is released.
The Alesis modules only knows and sends the Note off command on choking and Superior Drummer is designed to await an Aftertouch (you can read it in the SD manual on page 49) and plays a different sound, like you hear it. Other than apps like BFD, SD doesn't automatically blend between the two sounds, so you always hear the crash sound cutting off and then the "Mute" sound coming in with full attack at offset zero.
What you can do (but you'll have to do this for every SD kit you'll play): Go to the Construct page, select your crash, go to the Instrument section, activate "Edit articulation only", select the "Mute" articulation from the menu above. Then go to the Envelope section, activate it and tweak the different offset (i.e. at 140ms), attack (85ms), release and decay parameters until you'll get a nice, nearly unhearable blending between the crash and mute sound.
My values are only a starting point, it all depends on your power, trigger settings and the sound of the specific cymbal in SD.
Wish you luck!