A botanical puzzle.

This is Pampas Grass. It comes from Argentina and southern Brazil. I assume it grows there as temperatures rise in the Spring. Here it grows vigorously in September as temperatures fall. It looks good for most of our winter.
It seems to be triggered by a time clock which it has brought with it rather than by temperature.

And yet I have several varieties of Cacti which come from South America. They start their annual growth in April as it gets warmer.

Am I missing some obvious explanation?