You will need a transition piece of some sort. It is the nature of the beast. A laid ceramic/porcelain tile often takes up 1/2" of height when finished. To add any form of substrate (which you will need) you will add more height. It is the nature of tile.

Even if you get the two floors to sit flush, you will still need a transition through the doorway. That means you can choose to bang your head against the wall and try, try, try to figure out how to lay a tile floor over different formats of plywood/cement board or you can go ahead and do the project exactly as you had planned but with a slight floor height raise and a "reducer" as a transition strip that sits in the doorway. No head injuries required.

To get this to sit flush, you could be adding hundreds of dollars to a project that could be done quickly and properly with only a 1/4" (or less) difference and a very simple and inexpesive "reducer" sitting in the doorway...like most other bathroom/hardwood floor transitions have.

We start worrying about 1/2" differences or greater in a regular home renovation. A 1/4" or less is not a huge issue. Only in homes with wheelchair bound clients or clients with walkers and/or a "drop foot" is this type of floor height difference of "great importance". At that point, we pull out all the stops; use the thinnest, toughest, most expensive product and work our @55es off to get this thing to sit flush. And the client pays for all this effort as well. This doesn't come cheap.

And we get a professional tile setter to get it to that point. Or we use 1/2" plywood and linoleum/vinyl (identical to what you just pulled out) to get this to work. You've already bought the tile. Personally I would get it to sit as low as the technical specifications allow and use a very simple, hardly noticeable reducer and be done with it. After a year you won't even remember why you fought so hard to get this to "work".