What I see on the LCD is not the same I see on my...

Question

I've have been transferring a few movies via Adobe Premiere and I recognized that the video, when played on the computer, shows some things on the edges that were originally kept out of the framing. What is really bizarre is that they still don't appear on the LCD, viewfinder or even on the TV, only on the computer. Because I'm doing a film which framing is very important, I would like to know how, at the end, it would appear on the screen...