I teach my students to use a pic from the very beginning. They are not introduced to "pallions" until they start to solder their bezels to the back plates for their rings.
What lucky students and right you are. I also learned to work with
a solder pick before using pallions and it is really a breeze once you
have mastered it. I also learned to tack solder things using very tiny
solder dots on a pick then wire solder the rest of it. Wire soldering
is also something that not a lot of instructors teach and it too has
its uses and makes doing large pieces much quicker to solder.
However, I would add that each person I’ve studied with has his own
bag of tricks for soldering and no two people seem to approach it the
same. Some people hang large jump rings down and drop the solder on
the joint, some hold the jump ring with the joint at the top first,
stick the solder on with a pick, then reverse the ring and draw the
solder through the joint, while some lay the rings flat, place the
pallion under the joint and heat from the top to draw it through.
Bottom line I think is you simply have to practice, pratice and
pratice some more and find what works best for you.