Music and Content ID, plainly
Soundtrack.Today sells direct licenses from the rights holder. Content-ID state is per recording and per master file: when the rights holder has verified that the exact recording you license is not submitted to YouTube Content ID, the track page says so explicitly — "Soundtrack.Today does not submit this verified recording to Content ID." Where you do not see that note, no statement is made.
One honest caveat: third-party or erroneous claims can never be excluded absolutely — no catalogue on earth controls what unrelated parties upload. If it ever happens with music licensed here, contact us and we will help you dispute it.
When you license a track you receive the master-quality file plus a verifiable license code anyone can check.