On the A319/320 the
FACs generate a windshear warning whenever the aircraft's predicted energy level falls below a predetermined threshold.
On our 319/320’s we have EGPWS however the windshear warning is a basic GPWS function (Modes 1-6 and windshear) It is not an EGPWS function. It could your company enabled (paid for) EGPWS mode 7 an advanced windshear warning function which the EGPWS generates.
This is a very good explanation:
Mark V and Mark VII EGPWS Pilot's Guide
https://skybrary.aero/bookshelf/books/3364.pdf