Lindenmayer systems make all substitutions at once; this is one of their defining features. This is mentioned in the book The Algorithmic Beauty of Plants on page 3 of chapter 1, "In Chomsky grammars productions are applied sequentially, whereas in L-systems they are applied in parallel and simultaneously replace all letters in a given word." This book is one of the go to references for L-Systems (other than Lindenmayer's original papers in computational biology).
There is no order of precedence in the substitution. The sequence should be
a -> ba -> ccbba -> aaccbba -> babaaaccbccb -> ccbbaccbbababaaaccbaaccb ->....
if the rules
a -> ba
b -> ccb
c -> a
are applied all at once at each step, as they should be for all L-Systems.
I'm gonna write the evolution again blocked out so that each substitution is in brackets.
a -> [a] -> [ba] -> ba -> [b][a] -> [ccb][ba] -> ccbba -> [c][c][b][b][a]
-> [a][a][ccb][ccb][ba] -> aaccbccbba -> etc.
are applied. Please inform your instructor or T.A. that they have made a serious error in their study guide. Such an error could dissuade students from learning the material - especially introverted students or underrepresented students such as women and minorities. The student might think that the error is in their understanding or even capacity to understand rather than with the educator's carelessness. Out of curiosity how did this topic come up/what type of class?
(there is a small chance that your professor may have been referring to second order or even contextual L-systems which are more complex, but if s/he were referring to that they would have listed more axioms).