Paul speaking to believers, Christians:
Therefore, my beloved, just as you have always obeyed me, not only in my presence, but much more now in my absence, work out your own salvation with fear and trembling; for it is God who is at work in you, enabling you both to will and to work for his good pleasure. (Phil 2:12-13, NRSV)
Yes this is written to believers, my statement was concerning initial saving faith placed in the completed work of Christ Jesus to receive the gift of salvation.