Why do birds suddenly appear?

Note: This is not the first time I've asked this question.

I've just come back from a trip to Longfeng Temple, a Buddhist establishment in Pingtung which I visit from time to time due to its congenial spirit. This time, an iconographic detail jumped out at me which I had never really noticed before. There are three statues of Guanyin Bodhisattva there, and in each case she has a book on her left and some sort of bird on her right. I've never seen her portrayed this way anywhere else, only at Longfeng.

I became very curioua about the identity of this bird, but no one seemed to know what it was. I checked the Internet, but the only bird I could find that was associated with Guanyin was the white cockatoo in some Southeast Asian countries, and this was clearly not a cockatoo. Nor was it a Chinese phoenix, a Garuda bird, or any of the other usual suspects. I decided that, despite the strangeness of associating that bird with Guanyin, it must be an eagle.

No sooner had I thought this than I heard a shrill cry from overhead, unmistakably that of an eagle in mating season. I looked up to see two huge golden eagles, obviously a mated pair, circling in the sky. Eagles of any kind are a rarity in Taiwan -- these were the first eagles I had seen after 17 years in this country -- and golden eagles are particularly uncommon, listed in bird books as occurring in Taiwan only "accidentally." Yet there they were, and just after I had been thinking about eagles.

Later I asked one of the temple staff, and she told me that Guanyin's avian attendant was not an eagle but a Dapengniao -- that is, a mythical bird of enormous size (wingspan measured in thousands of miles), which in its larval form is an equally enormous fish called a Kun. Fortunately I had been ignorant enough to think it was an eagle, or who knows what I might have summoned!