CIRBaptist:
If you look at the orginal greek in which Philippians was written in the word that was used for salvation was the word: sōtēria
This word is translated to:deliverance, preservation, safety as the present possession,
It is talking about our already existing salvation. So they already have it. What does this mean though, working out our existing salvation with fear and trembling?
It is no coincidence that it jumps from working out our salvation right to verse 13 "for it is God who is at work in you, both to will and to work for {His} good pleasure." If you were to glance over this you would think that there is huge change in subject here between these verses, but these verses are closely related. Notice the word "for" as the start of verse 13. This is important to notice, because it tells you that verse 13 is a result of verse 12. This means that you can't read verse 12 and have the full context of the verse without verse 13. Also, notice that verse 12 starts with "So then". This is telling you that this verse relates to either the previous verse or all of the previous verses/subject matter that Paul was talking about before.
A lot of Christians like to separate verses from their contextual verses, but these conjunctionl words are extremely important if you are to get the proper context for each verse.
Based on what Paul is said before, (him being in prison under praetorian guard to emperor Nero[written in 60-62 AD]) and the struggles that he himself was going through I believe he was talking about working through the existing struggles of keeping hold of your salvation, not allowing anything in your life that would prevent God from doing His work in you.
Hopefully this helps.
Blessings!