Bagworms disappeared?

Hi folks - hoping someone with some bagworm experience can maybe shed some light on this...
We have a mid-size Arborvitae and recently discovered a substantial infestation of bagworms. We started picking them off but realized we might miss some and the tree was already starting to show major signs of damage (brown areas, etc). So, I never love doing this, but did a quick spray over the entire tree with some Sevin type insect killer. Afterwards we could see some of the worms climbing around...possibly trying to move their bags? Anyway, a day later, they seemed to all be dead - no bags moving on the tree. A day or so AFTER this, we came back to still remove the bags (so-as to remove any eggs from the area), and it appears all the bags are now empty? There are no worms to be found, dead or alive. I'm 'happy' about this, but also perplexed as to where they went? I have yet to find a dead worm on the ground near the tree. Now, i will say that we witnessed several birds that would perch nearby and fly to the tree, snatch a worm, fly away. This was BEFORE we sprayed. Is it possible they ate up all the worms that may have dropped from their bags, and/or eventually died partially out of their bags?
My biggest concern here, of course, would be that the worm population made its way to a new host plant and I'll find this out later in the season! Thanks for any help you can give.

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