Your Phalaenopsis does indeed have a "new arrival", called a keiki. Keiki is Hawaiian for baby I think. I don't grow many Phal. but have had numerous keiki. The rule of thumb as I understand it is to wait until the keiki has two or more roots and those roots are at least 2" long. You can then cut the flower/keiki stem just below the keiki, and pot up the new arrival.
