You're not making any sense. Frames are sampled at their "beginning", so naturally if you trim on frame 20 and zoom in, there will be some are right of the timeline indicator - the rest of frame 20's duration in real physical time. This is nothing wrong and has forever worked this way unless you are describing something else. Of course we don't know anything about your footage interpretation or comp framerate, so there could be some problem if you make a mess...
I think you're making a very common mistake for a newcomer: the first frame of a video is frame ZERO. It is NOT frame one.
Thus, 20 frames of video runs from 0-19, and not 1-20. Does this make a difference in your comp?
You can set the starting frame number to 1 if you want. Just change the start timecode in the Composition Settings panel.