Which video player are you using and are the subtitles embedded in the file or external (which means you can switch them off and on) or are they hardcoded?
Does not happen for me in Safari on Yosemite.
Do you have auto brightness on?
I am using Safari on Yosemite as well. Could you try and see if this happens on House of Cards Season 3 Episode 3 from 43:25 to 43:50?
Sorry, but my not US Netflix does not allow me season 3 yet. Luckily it was available via other means. When do they get their **** together, seeing as I could watch Sense8 on the day of the release and am now watching Grace & Frankie. Idiots.
Tried another browser to see if the problem is "universal"?