The buffer pool never spills to TempDB.

If pages are read in from disk for a table and there's not space in the buffer pool, other pages will be removed from it, maybe even pages of the same table that have already been read by the query processor.

What spills to tempDB are sorts, hashes, exchanges, spools (though they're temp structures anyway, so they can't exactly be said to spool).

Temp tables will be written to TempDB if necessary