Effects do not affect your original clips in Project panel. If you want to see the result of your colour correction, you should use the sequence, within which your colour correction was applied.
In multicam scenario you can colour correct in several ways:
1. Apply color correction within your master sequence (either onto individual cuts or on an adjustment layer) when you're done with cutting.
2. Apply your colour correction onto clips within particular camera angle. If you want to use an adjustment layer, you have to nest that camera angle with adjustment layer first and then use that (those) nested sequence(s) to build a sequence out of colour corrected camera angles.