A compressor (not side chained) lowers the signal of the loudest sections making the overall signal have less volume and also sound less loud. After that happens there is usually a gain stage where you can boost the level of the overall signal. If you were to boost the signal back to the same volume it will sound louder than before. This is because those loudest sections have been boosted back to where they started while the previously softer sections have had their levels increased by the gain stage - so the overall signal now sounds louder.
Using side chaining to duck the signal you don’t want to increase increase the gain after the compression occurs. If that happens, even if only on a frequency range, it will sound louder. So make sure that isn’t happening. Some compressors have an auto “makeup” feature (actual names are all over the place) that you’d want off. Other compressors will always auto makeup the gain as part of their design & not give you a choice - don’t use those for this application. Some compressors also have an initial gain stage before the compression to raise the incoming signal which would also make it sound louder. This initial gain control is sometimes used to set the compression.
Try muting any signal into the side chain, which means no compression will occur. Then adjust the gain(s) in your compressor so the signal is the same when the compressor is bypassed or engaged. Now try setting your compression using the side chain.
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