why not return the vinyl tiles and install
ceramic tiles?

Judging from other houses I've seen lately, I must be the only person
in the U.S. who is not a fan of ceramic floor tiles. Never liked it!

But I appreciate your input about putting thinset (or, probably more
appropriate in this case) Armstrong vinyl tile adhesive down over the
black mastic. I had considered relaying the 9x9 tiles I took up,
since 90% of them are intact. It's good to know the thinset will hold
them to the black mastic. That would keep whatever asbestos is down
there in check. Then I could lay the new self-stick vinyl ones on top
of the secure old tiles.....my original plan anyway.