The Youtube terms of service allow you to play music, and they do not impose any condition to the effect that you have to be alone in a soundproof room to play music. The school district might have a rule prohibiting the playing of music on school grounds (presumably with an exception for music classes), but there are too many school districts in Alabama to research that question. You might ask the superintendent of your local district about such rules, if it's important. Copyright law does include a separate requirement for permission to perform publicly, for example the music played in a store requires a performance license. Under 17 USC 106(4), the copyright owner has the exclusive right to authorize a person "to perform the copyrighted work publicly". The definitions section says what it means to perform publicly:
(1) to perform or display it at a place open to the public or at any
place where a substantial number of persons outside of a normal circle
of a family and its social acquaintances is gathered; or
(2) to transmit or otherwise communicate a performance or display of
the work to a place specified by clause (1) or to the public, by means
of any device or process, whether the members of the public capable of
receiving the performance or display receive it in the same place or
in separate places and at the same time or at different times.
It does seem that we're in the realm of a "public performance", since the law does not specifically say "intentionally play so that others can hear it" (we don't know whether the teacher is being unintentionally overheard). However, the purpose of the performance license is to cover businesses that rely on playing music to make a buck, and is not intended to force people to watch out if strangers / co-workers are listening. There is a classroom-use exception, whereby teachers can perform music for instructional purposes, which this probably isn't.
However, the Youtube TOS does say that all content-providers
also grant each other user of the Service a worldwide, non-exclusive,
royalty-free licence to access your Content through the Service, and
to use that Content (including to reproduce, distribute, modify,
display, and perform it) only as enabled by a feature of the Service.
Therefore the teacher has permission to perform: except if the content is illegally uploaded by someone lacking the right to grant permissions (and to upload, in general).
If you suspect that someone has illegally uploaded some artist's content to Youtube, you can contact the copyright holder with relevant information. They may or may not pursue a DMCA takedown; if they do, and they are really gung-ho, they could try go to recover lost licensing revenue. It isn't clear that there is a license for "teacher laying music that others can hear".