The sentence taken from your audio book is 100% correct. In English, the verb become doesn't require a reflective pronoun, EXCEPT when being used to emphasize the subject (see the following examples):
>He himself didn't become a branch manager of this company until 2003.< (Himself here is used to only emphasize the subject "he" - (Note!) not a reflective pronoun.
>Megan would never go outside without a jacket in this chilly weather herself .< (Herself here is used to emphasize the subject "Megan" - therefore not a reflective pronoun.)
Now back to your other question(s):
"Prior to YOU becoming a manager, ....." is wrong because becoming a manager is a gerund phrase; therefore genitive (YOUR) is needed before it (CORRECT: prior to YOUR becoming a manager, ....). However, people usually don't use a genitive here to just keep the whole sentence simple and tidy.
"Prior to becoming YOURSELF a manager" does sound a little awkward (BETTER: prior to becoming a manager YOURSELF, ....). Again, a simple and tidy sentence without any whistles and bells sounds so much better (only my personal style), especially in this case.
Anyway, just my two cents! I'm sure the other teachers will have better suggestions/explanations than mine above. Let's wait and see what they have to say .......
Student or Learner