Hi
You seem to be confused regarding the two screens... 
The LEFT hand screen previews the selected clip (irrespective of where it is) and allows it to be trimmed etc.Only the selected clip is played in this screen.
The RIGHT hand screen previews the project or the clips when they are on the timeline, (the sequence line) and what is seen there depends on position of the red cursor line. The whole sequence of clips on the timeline is played in this screen.
e.g.
If you have selected a clip in the media list then it will preview in the LEFT hand screen. It will not be visible in the right hand screen until it has been placed on the timeline. You can drag and drop it onto the timeline if you wish and trim it there.....or....as you seem to be doing...
Trim it beforehand in the LEFT hand screen by pulling the red IN marker to the right and pulling the blue OUT marker to the left.
This will trim the clip as shown by the extent of the green bar which is under the thumbnails.
Clicking the green down - arrow will now place the trimmed clip onto the timeline (or sequence line) where, by default it will be selected. (shown by it turning blue) and will now appear in the RIGHT hand screen. The right hand screen is used to preview your PROJECT, i.e. all the clips that are on the timeline.
Nat