Thanks for your replies guys.
Ultimately, I’m looking to exclude certain tracks from chasing MIDI events (especially MIDI notes). The reason is that MIDI chase of notes is mostly useful for pads and string instruments but much less useful for plucks and percussion. Currently, if I hit play somewhere within a beat, a bunch of drum sounds trigger suddenly due to MIDI chase in addition to pads, and atmospheric sounds.
Currently, it does seem that Cubase has only a Global On/Off option.
As per the Logic manual link above under “Avoid triggering sampler drum loops when chasing note events”, you can see that Logic allows you to avoid MIDI chase on particular tracks. The manual specifically mentions drum loops as this is a good example of a type of track where chase is not useful.