The chord scale system, though common in jazz, is not used (or even heard of) in "classical" music
Yes it is. They just don't tell you about it until you are a long way into your studies, or teach you how to use/apply it to your instrument for even longer.. At least that was my experience, its because all the notes are written on the score in front of you you don't need to know whats going on harmonically to get by.
4th grade theory brings in cadences, which is the beginnings of this. The classical system notates chords in a slightly different way to what is commonly used in jazz or pop music though. You also start doing technical work in the high grades, things like dominant 7th arpeggios on, and of a given note.
And you don't touch on things in theory until 6th and 7th grade that are jazz 101.
Either way...
Generally, if you run into a chord outside the scale the music has probably modulated to a new key at least temporarily. You just have to find the new scale.
Thats the best I can explain without there being an actual example to look at.