"This season" identifies a period without focussing on its duration.
"All season", with the "all", stresses the duration, and corresponds with your teacher's explanation of the pr.pf.cont. tense.
Very loosely, it is like the difference between "a century" and "one hundred years". A century (a period) lasts "for one hundred years" (its duration). Similarly, "this season" (the current season, period) lasts "all season" (however long that may be, duration).
If you want to emphasize that she's been playing for this whole season rather than, perhaps, the last one, you can say "she has been playing with the orchestra all this season". If you just want to say she has played with the orchestra this season, without mentioning duration ("whole" or "part of") at all, you can say "she has played with the orchestra this season".
PS If you are still confused about the difference between a period and its duration, consider the period during which the Ming Dynasty ruled China. Let's call it the Ming Era. We can talk about the Ming Era without knowing precisely how long it lasted. But in fact, the usual dates for the Ming Era in the Western calendar are AD 1368 to 1644, so the duration of the Ming Era is 276 years. In the example above, "this season" and "last season" are periods, and "all season" is the duration of a season, although we don't specify exactly how long: say X weeks.