I think "Sith" and "Jedi" are customary labels for preferences in interacting with the Force, they're not really things-as-things even as much as a concept like "Earth tones" can be said to be. Someone like Mace Windu was pretty obviously sith by inclination, even though serving as a cultural-institution jedi. (Leia, too, is pretty obviously much more sith than not in their approach to the Force; passion, intuition, and honesty, rather than composure, perception, and compassion.) The historical jedi were hopelessly corrupt through expediency; right-action turned into "what does the Senate want?", rather than what your perception and intuition show you from a state of detachment. The historical sith were hopelessly corrupt through ambition toward control; right-action turns into "my passion is of supreme importance". I don't think that makes being a sith-inclined Force user inherently corrupt; there's presumably a lot of ways to be passionate, honest, and intuitive and an OK space wizard.

Kylo is totally making the "my passion is of supreme importance" error, which is an interesting parallel to Luke (who is doing the same thing, only the passion is self-loathing about error and the possibility of further error). (I think that's an intentional parallel.) So, no, no "turning to the Dark Side" eye-effects, but I think it's legitimately being coded as a Sith way to fail. It's certainly not the jedi error of trying to generalize compassion to the statistical mass.