This understanding is taking things out of context. In fact, this is only part of a sentence, which doesn't end with that verse. This verse is found in Philippians 2:12. Let me first quote the whole sentence which continues in verse 13.
12 Therefore, my dear friends, as you have always obeyed—not only in my presence, but now much more in my absence—continue to work out your salvation with fear and trembling, 13 for it is God who works in you to will and to act according to his good purpose.
Note that the rest of the sentence seems to contradict how may apply the previous phrase. It represents a thought that plagues the debate, asserting that God's will and man's will are mutually exclusive (i.e. if God has a will, he imposes it on man, who becomes a mere robot or puppet), thus creating a false dilema. Jonah had a will and ran from God's plan for him, but God brought him back through a number of means into His will, and he went to preach to Ninevah.
So what does "work out your salvation" mean then? I would suggest that it means to reflect the grace you have received for your salvation through faith. God gave you salvation through faith as a free gift, not by works. Therefore, you should respond by continuing to grow in your sanctification through obedience to show your gratitude for God's incredible gift to you. As we work this out and grow, we reflect God's grace even more, and serve as witnesses to glorify God.
