I just watched that clip on the one i have using only the in built speakers and the lips do not match up with the audio.
I just randomingly chose a video:
play that on your one with the inbuilt speakers. you should not see any lip delay with the audio.
again, i think what you are experiencing will happen from random videos. does not matter who or what entity uploaded them. It is no fault of the app or the device, as witnessed by the clip I just linked above.
i did not know you purchased it second hand. was it rooted? Curious, why did the guy sell it?