1/2 inch plywood is not adequate for 12 inch tiles.

It has excessive flex between the joists.

Half inch flooring is not OK. Minimum standards call for 1 1/8" with appropriate 1/4" Durock or Hardi to bond the tile.

If the vinyl is tight as a rock, you can add the 5/8 over it. No glue, but screw it thoroughly. I usually go about every 8" around the perimeter and about 10" in the field.

Using a 1/4" trowel, spread a creamy mix of thinset over it and install the concrete board, screwing it immediately in the same manner as above. Stagger this board, overlapping the plywood seams.

1/4" board is fine for floors. The thicker stuff is generally for walls. Hope this helps.

I installed ceramic tile some years ago over a subfloor of beams on 16" spacing, 3/4" solid wood spaced planks, covered by 3/8" plywood - total thickness about 1 1/8". I stripped the vinyl cushion flooring first. It was installed with a thinset said to be suitable for a flexible floor.

Net result is that it is too flexible. The grout cracks, loosens, and falls out. Some tiles have come loose and have even cracked.

My experience suggests you should remove the vinyl for sure. I recently installed some marble tile over the same floor. This time I used thinset covered by 1/4" cement board, and screwed it every 6". Too soon to tell if it stands up over time, but it feels much more solid. For the cost difference if you can afford the extra thickness of 1/2" cement board, I would go with it. It was going to cause me a problem so I went with 1/4", and hope I don't get stung again.

Removing vinyl sometimes can be made much easier if you cut slits in the vinyl surface every 1" and then mop lots of soapy water on it. Then scrape it up after it starts to curl up.