How to know if mysql tmpdir is being used
In *nix, a file can be creat'd, rm'd, then written to and read from by the same process.  No flavor of ls can see it, since it is already rm'd from the directory, yet the program can see it.  This is a trick that makes sure that the file is not left behind if the program crashes.  MySQL often uses the rm trick.

ls cannot see the rm'd-but-not-closed files, but lsof can see them as (deleted).

df will change because of the space being consumed.

If you show us the SELECT, SHOW CREATE TABLE and EXPLAIN SELECT.  We may be able to give you tips on avoiding the tmp table.  (I assume your real question is about performance?)