It seems to me that Illustrator is not properly handling metrics in variable fonts. First I though it was about a missing HVAR but even with that it is keeping the metrics of the default layer.
Photoshop handles the same fonts just fine (with the exception of AmstelvarAlpha-VF-2017-01-23, that is not shown in the font menu of Photoshop but works in Illustrator).
(Where would be the best place to report those problems?)
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https://github.com/adobe-fonts/adobe-variable-font-prototype
If those fonts don't work properly, then it must be a bug in AI or PS. But if they work, maybe something is missing in the fonts.