Thanks for both emails. Basil "fixed" my problem:
Apparently I have two fonts installed on my system --- "Tibetan Machine Uni" and "Tibetan Machine Unicode", the and the former displays things correctly while the latter does not. I'm sorry for bothering you with this, but until I received Basil's reply, I hadn't realized that these are two fonts...

Thanks again, and sorry for the alarm!

Mayer

On Sat, Jun 1, 2019 at 9:11 PM Eli Zaretskii <eliz@gnu.org> wrote:
> From: "Basil L. Contovounesios" <contovob@tcd.ie>
> Date: Sat, 01 Jun 2019 19:04:43 +0100
> Cc: 36020@debbugs.gnu.org
>
> FWIW, I can't seem to reproduce this on the Emacs master and emacs-26
> branches (build info follows my signature).  Here's what I tried after
> installing the fonts-tibetan-machine package on Debian:

We don't know the Emacs version of the OP.  In addition, it could be
due to a difference in the installed versions of the m17n-flt library.