I just did this in my kitchen last week and so far all is good. I had
a solid sub floor (1X6s below 3/4 plywood) that had 1950s vintage
linoleum which I was afraid could be asbestos, so I decided to
encapsulate it. The vinyl was in good shape with great adhesion. I
did fix all squeaks with 2 1/2" drywall screws before beginning.

I used Mapei Ultraflex II thinset (polymer modified as you mentioned)
under hardibacker board which was fastened with many screws. I filled
the joints between the hardibacker board with thinset and fiberglass
drywall tape when I put down the tile. Make sure your thinset says it
is acceptable for vinyl. Also check out the hardibacker.com website
for additional instructions.