If you want to transfer colonists from (click a "ship" icon on) a multi-species colony the "Embark population" dialog is called. If from single-species - just picks a single "unit" (the "old" way). The "old" way has disadvantages - you can't pick more than one in a single "transaction", and the "focus" (the lower third of the screen) immediately switches to the "source" system (very inconvenient).
Is there (or could you make) a way to always/forcibly call the "Embark population" dialog after clicking the "ship" icon?