The answer as given by the JSTree developer on his Github:
The type is not read off of the rel attribute. Try using
<li data-jstree='{ "type" : "floor" }'...
in your markup (and keep the single quotes outside, and the double quotes - inside for the data-jstree attribute).
See: https://github.com/vakata/jstree/issues/497
In my case I was just using the types plugin to overwrite the icon. Turns out this can be done by simply giving the list item an data-jstree property with an icon property set.
<li data-jstree='{ "icon" : "icon.png" }'></li>
Hope someone finds this useful in the future :)