Perhaps a slight (grammatically sound) rearranging of the phrase might help clarify:
let the outworking of your salvation be with fear and trembling,
A few clues from the context tell us this phrasing (and hence meaning) are correct:
"Therefore, my beloved, as you have always obeyed.."
Paul was directing this letter to those who had "always obeyed" and were his beloved. In other words, it is directed to believers in the church at Philippi. If there is confusion as to whether he is referring to "working towards" your salvation, the next verse (which is still the same sentence, by the way) clarifies that right away:
Philippians 2:13 for it is God who works in you both to will and to do for His good pleasure.
So, "work out(wardly) what God is working in you" is perhaps the simplest way to understand the meaning Paul was trying to convey. If that is still not clear enough, we can always go to the previous chapter where we find this:
Philippians 1:6 being confident of this very thing, that He who has begun a good work in you will complete it until the day of Jesus Christ;
In other words, it is God who begins, and completes the "good" work (ie, salvation and sanctification) in believers. So, again, the "working out" of a believer's salvation is the "outworking" of something that has been done in them. Hope that helps.