DVCO has phase reset. It is depicted by the dot at the start of the wave shape image.
BD Sharp also has it (same thing)
The filter will filter out any signal that goes through it. As the tone of the click does not change in any way (when lowering LP cutoff), then the click must be generated after the filter.
I also like clicks when I intend them to be there but only when they are consistent for each trigger. Having a transient change character for each hit is not good.
Maybe the answer is something about the AMP envelope reset that you mentioned. I am not sure I have a full understanding of this feature yet. Could you please explain it in more detail? What exactly happens in each ADSR stage and when is it relevant?