Update: the new version is already on CTAN.
It's a bug with Asana Math. I've contacted Apostolos Syropoulos, the author, and he'll probably release a new version soon.
The issue (which I uncovered thanks to Khaled Hosny) is twofold. First, unlike other TeX Fonts, but like Cambria Math, Asana has multiple versions of its big math operators. Usually there's only one, which is the
\displaystyle version of the operator. This can be seen by opening the font in fontforge and looking at its MATH table, in the section vertical variants.
The second part is that the font constant
DisplayOperatorMinHeight was set too high, to 1850. As the name indicates, this constant indicates the minimum height a glyph needs to be considered the display version of a math operator. But the "correct" display version of the \bigcap operator has a height of only 1559, thus not qualifying for display. The engine then looked for the next version, which has heigh 2588, and selected it. This is the huge glyph you're seeing.
The first part is important because if there weren't other variations, the engine would just settle for the "small" display operator.
If you can't wait for the bugfix release of Asana and are using luatex, the font can be patched on-the-fly with this code (copied from here):
local function patch_asana(fontdata)
local mc = fontdata.MathConstants
if mc then
mc.DisplayOperatorMinHeight = 1337
luatexbase.add_to_callback("luaotfload.patch_font", patch_asana, "patch_asana")