Yes, Captured Bugblatter’s ability triggers on its own death. The short reason why is that the rulings say so. The long reason why is in this post in the Rules thread, under the multiple abilities heading.
Huh… that’s very different from how I would interpret the rules; thanks!
Feral Strike for 2 Blooming Ancients results in two Blooming Ancients arriving with +1 Rune each, because they really do happen simultaneously and so they each see the other one arrive.