What kind of underlayment material is this?
Underneath vinyl tile (which if old enough may contain asbestos) was usually either rosin paper, hardboard, or cutback.
Rosin paper is really thin and tears up into annoying little pieces. It's more or less readily identifiable; certainly not easily mistaken as either of the other two.
Hardboard is &quot;often used as underlayment. Likely 1/8&quot; thick. If so, you can remove or go over if in decent shape&quot; with basically any type of flooring besides real tile.
Cutback... gah, is &quot;that black tar stuff&quot; which may or may not also contain asbestos.

Asphaltic cutback adhesive is an older type of mastic made with asphalt-based cement. As a petroleum-based material, the cutback is not softened by water. Some cutback adhesives contained asbestos. source



can be very difficult to remove unless you use shot-blasting equipment. Fortunately, most grout and mortar manufacturers make a thinset which will bond to &quot;cut back&quot; adhesive.
Typically, the &quot;cut back&quot; should be scraped smooth so the tile is not sitting on ridges of adhesive - although it does not have to be absolutely flat. Note, not all thinsets will bond to cutback so it is important to make sure the thinset used is made for that purpose.
Also, the adhesive must be true &quot;cut back.&quot; That means it was made from asphaltic material, is not water sensitive, and will not soften when exposed to water. There are also black-colored latex-based vinyl adhesives that will not hold up under ceramic tile if they get wet. source



[If laying down new vinyl, the] plasticizers in the vinyl migrate down through and attack the Cutback Adhesive which softens it and then the cutback starts migrating up, causing staining in the vinyl flooring. Cutback Adhesive residue will also eventually bleed up through a felt-backed flooring product as well.  source

It's easier to just rip up the subfloor if it's cutback. When I had to remove it from concrete, it required a scraper blade in an SDS (rotary) chipping hammer drill, a commercial floor machine with an abrasive pad, and several days of labor for a single room. Mineral spirits just made it gooey and even harder to scrape up, aside from being noxious and a fire hazard.