tiling over cutback adhesive residue
Although anything is possible, parquet was not generally installed using cutback adhesive. It may be dark, but it may be the kind that actually dries hard which cutback does not.
If it is cutback, you can still install tiles on that floor with a little prep. You'll need to remove the cutback until only a film is left. In other words until you start to see the concrete. You'll need a wallpaper scraper which has a razor cutting edge and several hours of your time. Do not use any chemicals or solvents, they will soak into the concrete creating a bond break.
Either of the products you mentioned will be fine after the prep of the old floor and for the other area too.
You can mix by hand with a piece of 1x2 lumber or a margin trowel. Be sure to add the powder to the water already in the bucket. Of course a mixing paddle along with a good HD 1/2" variable speed drill motor is preferred. Mix at slow speed under 300 rpm.
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