Thanks!
I found the possible cause, and possible solution too. It is not the plugin at fault actually. I discovered, where the plugin shortcode is rendered, the content must be cached somewhere, as the plugin code is simply not executed. Later on, when the plugin checks to enqueue it’s assets, it finds nothing, as if the shortcode was never executed at all (but yet it is on the page, so it must have been printed statically)
If you are using any frangemented cache or anything, that may cache only parts of the page, I strongly recommend turning that off.
Anyways, the solution was to change the CSS loading method back to the old one.