After a first filler procedure for under-eye bags, is it best to underfill than overfill, and go back to get a touch-up?

I definitely prefer the less is more approach when treating underneath the eyes with fillers. It is always easier to add more than to take away too much (even though hyaluronic acid fillers are dissolvable). One syringe of filler is enough to make at least some improvement underneath the eyes. Unless the filler wasn't injected in the correct place, then that's a whole different story. I would give it 2 weeks and then follow up with your injector. If more is needed then it can be given at that time. Hope this helps answer your question.

One syringe is usually enough for under eyes but not if it was injected in the cheeks.  It is good idea to undercorrect and be conservative.See an oculoplastic specialist for eyelid filler injection.