In the original Starling version of Feathers UI, I had a concept of "effects", which were similar to transitions, but they're meant for a single display object (transitions are meant for two display objects). For instance, you could define an addedEffect that would play an animation when a component was added to the stage. This would also work when adding a pop-up. However, I haven't ported those to the newer OpenFL version of Feathers UI yet. I may add them in the future, but I want to rework some things if I do, so it's not coming any time soon.
In the meantime, you can just use Actuate (or another animation library, if you prefer) to do something similar.
For instance, if you want a component to fade in, you should be able to do it pretty easily like this:
component.alpha = 0.0;
Actuate.tween(component, 0.5, {alpha: 1.0});
PopUpManager.addPopUp(component, owner);