I've been studying up on mites, and I now think the mite might be the
southern red leaf mite, although it isn't recorded on buttonwood. It
is an "exceptionally destructive" pest of holly and azalea, introduced
into the US in 1917 and now found on the East coast and California. It
has been found on clethra, cleyera, elaeagnus, eucalyptus, eugenia,
grevillea, hibiscus, juniper, kalmia, oxalis, photinia, pyracantha,
rose, and viburnum. It causes bronze spots on leaves and eventually
death of the leaf and in severe cases, death of the whole plant.

Web sites recommend use of "appropriate miticides" (yeah, thanks!) and
use of dormant oil in winter. Dormant oil would be good, but of course
any plant should be tested for phytotoxicity before treatment, and the
oil shouldn't be used in warm weather.

So if your plant has distorted leaves and raised scabby patches or
flecking, get out a hand lens and look on the underside of the leaf for
mites. You'll probably have better luck seeing the cast-off white
exoskeletons than the mites themselves. Spider mites produce webs, but
lots of mites don't.

Nina.