The quote in question is not speaking of salvation, but of sanctification, that is, growing in God.
“The quote in question is not speaking of salvation ...”
That is your personal (and wrong) interpretation.
The quote from St. Paul to the Philippians used by St. Augustine to make his point here is that it is not enough to believe or have the true faith, but that we must strive and labour to the end in the way of perfection; secondly that St. Paul did not look upon himself as absolutely certain of his perfection, how much greater would this presumption be of us?
Notice it is not works instead of belief, it is BOTH that are required for perfection.
This is St. John Chrysostom’s exegesis and his position carries far more weight than the interpretation of some late date reformer.
St. Paul expected works along with belief: Colossians 3:25; Romans 2:6