Why aren't my triggers firing during an insert by SSIS?
Because the OLE DB Destination task uses a bulk insert, triggers are not fired by default. From BULK INSERT (MSDN):
If FIRE_TRIGGERS is not specified, no insert triggers execute.
One must manually specify FIRE_TRIGGERS as part of the OLE DB component through its Advanced Editor.
Then add "FIRE_TRIGGERS" to the value of FastLoadOptions (note that options are comma-separated):
With that option in place, the triggers should fire during the task's execution.
complementing ladenedge's answer.
Because the OLE DB Destination task uses a bulk insert, triggers are not fired by default
that is true when you have the "fast load" option selected.
If you change it to a regular "table or view" data access mode, your triggers should fire normally because the insert is done row-by-row