The cones stay on until the wind blows them off. The seeds spread through the wind, so it's beneficial for the species to keep the cones until at least the last seed was blown away.
This can take a while.. Like 4 years.
The cone however doesn't sense this whatsoever, once it's mature it's abscised internally by the tree and it's on the branch while being dead.
You can manually pick them off if you want.
Nice tree by the way.