I think i found the solution. It took me couple of days and a lot of Googling, to finally figure it.
It has got to do with MacOS(iOS) System Preferences, and how to show captions.
To fix this, go to:
Mac System Preferences -> Accessibility -> Captions -> Change "Transparent Background" to "Classic".
You will have to close the browser tab or application, for it to apply.
I discovered that the subtitles in the HTML player were without the background until the next morning, because I hadn't closed the tab before.
Had I changed the setting back, I wouldn't have found it out. :)