Right-click (or Control-click) on the relevant clip or clips in the associated Event. In the pop-up menu that appears, provided the option is available, select Optimize Video. Choose the most suitable size if more than one size is offered (for example, Full - Original Size or Large - 960 x 540).
Optimizing the video may fix the problem you are seeing with the Picture in Picture feature. It usually does the trick when this type of issue arises with the Cutaway feature.