You might have to be a little more specific as to the model you're using. Everio is a whole JVC product line of past and current digital video camera models, recording in different formats and onto different media, including standard definition MPEG-2 cameras as well as AVCHD cameras. Have a look here:
That said, if you go for the "biggest" and newest version that is available of Movie Edit Pro right now, which is Movie Edit Pro 15 Plus, you should have all of these formats covered. I guess you could also see whether you can test this for yourself. If you already own the JVC cam, just get a trial version of MEP 15+ from the Magix website. If you already own MEP 15+ but you don't have the video camera yet, it's a little more tricky. But maybe some store will give you the chance to try before you buy or to copy a few sample files off the camera and take them home with you.