Final Cut will only handle AVCHD files when it finds them in their original file structure (either by connecting the camcorder or using a memory card reader), not isolated .mts files.
Since we can’t import MTS file directly to iMovie, not to mention get editing there. We can try a workaround to transfer MTS files to other formats that iMovie imports like MPEG-4, MPEG-2, MOV, HDV or DV.
This can be realized by the powerful and professional AVCHD MTS to iMovie converter for Mac, not only you can transfer MTS files to iMovie supported file format with good quality and fast speed, but you can also do some editing on the file you want to convert, like cropping unwanted frame from clips, trimming the length of the file, adjusting Brightness, Contrast and Saturation of the file for your smooth editing.
Step by step to transfer MTS format files to iMovie
First Download and install MTS to iMovie Converter for Mac
Second How to transfer and import MTS format files to iMovie for editing on Mac.