Think about how the compressor does its job of reducing the dynamic range: You set a threshold where any peak above it is turned down in volume at a ratio of X:1, where X dB in is heard as 1 dB out. So 2:1 means every 2 dB above the threshold is output as 1 dB (so a sound going 4 dB over the threshold will come out only 2 dB above, etc., etc.). It doesn't normally cause an increase, because by decreasing the dynamic range you're actually lowering the ceiling on the overall volume.

Your compressor probably has an auto-makeup enabled for the gain, so as you are reducing the dynamic range and making the overall sound quieter, the program is turning up the output gain so that the peaks remain at their original volume - making everything that did not hit the compressor louder as a result.

If I were you, I'd go diving through the Mixing/Mastering subforum for the threads on compressors and watch a few videos on the specific effects of what a compressor does and how it does its job, and it should become more clear!