Were the Corinthians Paul rebuked actually believers?
Yes. The Corinthians whom Paul rebuked were believers. They had been born again and placed into the Body of Christ, yet were still fleshly minded and weak spiritually, so Paul called them carnal and babes, not unsaved. Scripture distinguishes this from Romans 8's use of carnal for the unsaved.
Les teaches that the word "carnal" in this context speaks of believers who have not really come out of the fleshly experience and are still under the control of the Old Adam rather than the Holy Spirit. In Romans chapter 8, Paul uses "carnal" for the unsaved individual, but here he is speaking of believers who are saved and in Christ, though still weak spiritually, even as babes. The milk analogy shows they needed basic teaching, not solid food. The Corinthians got Paul upset in his first and second letters because they were still steeped in the flesh, yet he calls them believers—born again, placed into the Body of Christ, but still fleshly minded. God expects growth from His children.