Depends on context. My best guess is that they are talking about drinking alcohol, where "Turn it up!" or "Turn up!" means to drink because you are "turning up" your glass. These days it might mean to drink everything in your hand. I'm older now, and I can't keep up with how fast pop culture changes English.

Apparently, he sings "turnt up", which is a slurry way of saying "turn it up", ie. turn up the volume. As much as I admit Dok2 is good at rapping, he sounds a little funny when he throws in English rap phrases - it's as if he's simply copying other rappers. There's a little bit of funny mispronunciation as well ("turnt" doesn't sound natural, even in slangy English). It's more like Konglish. To my native English ears, he doesn't sound "hardcore"... just "cute". Sorry to tell you that, if you're into his music.