To preface my comment I'm just going to say that I have dealt with computer/digital audio for roughly 35 years (although never an audio engineer)... I have never liked compressors and I won't try to pretend I can give good advice about the tool. They make audio sound artificially loud by "bunching up" waveforms into a a small span of the spectrum. I will use the Multipressor when I'm trying to reshape sound... but I find it rather complicated, so I tend not to give much advice about that plugin. Hopefully somebody with better compressor skills will chime in to give you better advice.
In the meantime:
You need to realize that all audio meters are based on ***relative*** scales. Final Cut uses two different scales right in the UI. The waveforms on the audio clips themselves have a +12dB overhead while the "standard" audio meters (on the right inspector column) have only a +6dB overhead. The audio is the same level throughout - just be aware there are two different metering systems at play (three if you count the compressor's meter).
It appears that the Compressor plugin you are using has an output meter with only a +3dB overhead. That should mean that a signal at 0dB will translate to a +3dB loudness in Final Cut — follow me? Adjust the output Limiter to at least -3dB or lower.
Most audio meters measure the same span of loudness. TECHNICALLY, 0dB is the "threshold of hearing" (at the bottom), however, as I've said, different "ruler levels" for audio are used by different tools. Final Cut Audio Meters set 0dB at the point of digital clipping. You often have to watch the "signal chain" to see how meters compare. The Compressor meter shows -5.8dB while the FCP audio meter shows (approximately) +1dB... so you may have to adjust the limiter output even lower than -3dB... based on:
Your **target** audio level, inside Final Cut, should be around -6dB for loud sounds (on the audio meters — there's still 6dB "overhead" to the 0dB mark); -10 to -12dB for "conversational" level audio. [Let the end user decide how much more Volume to apply with their computer settings! Audio should be comfortable to listen to at 50% Volume settings on your computer... and I'm figuring: with headphones here...] If you see red, you could damage someone's hearing... not to mention the audio...
HTH