It's just a matter of "idiomacy", not "grammar / syntax" as such. But as this chart shows, there's a marked preference for turning something back on, as opposed to turning it off again (rather than turning it back off and on again)...
Note that I only multiplied the hits for the off versions by 10 so they'd all fit on the same graph. We're only interested in the relative preference for the back / again versions - it's irrelevant that both off versions are less common than both on versions.
Syntactically, it's perfectly okay to speak of turning something back off (so long as it had previously1 been turned off on at least one occasion). We're just much more likely to speak of turning it off again.
1 Note that native speakers wouldn't usually include either again or back unless the referent had been explicitly "turned off" before. In OP's context, that doesn't seem to be the case (presumably, the speaker only turned the music off on a single occasion within the current "frame of reference").
But sometimes in such contexts we can use back or again to imply "reverting" (to some previous state), as opposed to repeating something that was done before.