Explore gets notfied of an abend by the CICS XPCABND Global User Exit. This is executed before a dump call is made. I took a transaction for which threshold messages were being correctly issued for AEXL abends and changed it from DUMP=YES to DUMP=NO using CEDA.
Now I no longer see thresholds and no trace entry is created for an abend.
In summary, we will not display ABEND threshold messages for transactions that have DUMP=NO, because the CICS exit isn't executed.