Make sure the Preview panel is properly set up. The composition frame rate should be set to Auto. That is indicated by the frame rate being enclosed in parentheses. If your comp is set to 23.976 the frame rate in the Preview Panel should look like this: (23.976). It should change when you change the frame rate in the composition.
One more thing. If you change the frame rate by selecting footage in the Project Panel and opening the Interpret Footage Panel, you change the playback speed. A 10-second clip shot at 30fps will take 10 seconds to playback in a 24 fps comp or in a 200 fps comp. The only thing matching footage frame rate to composition frame rate does is match the number of frames in both, Composition frame rate has nothing do to with playback speed. Keyframes and cuts are based on time. Cut a layer at 2 seconds, then change the frame rate of the comp from 30fps to 10fps or to 200fps and the cut or the keyframe will still be at 2 seconds. The frame number will change, but the time won't.
I hope this helps.