Premiere Pro issue with preview?
I don't use Premiere Pro, so I don't provide the step-by-step instruction, but I know the basis of your problem.

In your original (compressed) video they are so-called intra-frames (aka keyframes), which contains the full info about the particular frame, and other frames (inter-frames) which contain — simply said — only differences from the previous intra-frames.



In other words:


every intra-frame is independent of others frames, while 
non-intra-frames are dependent on the nearest previous intra-frame
(and — maybe — from other frames, too).


Let suppose there is 1 intra-frame every 10 seconds (i.e. at time stamps 0 s, 10 s, 20 s, etc.),
and the “other” frames are between them. 

Now, you want to cut the 20 s video from the time 13 s (i.e. the range 13 s – 33 s).

The frame at the position 13 s is not an intra-frame — it needs the previous intra-frame (at position 10 s) to obtain the full picture. 

So your software simply adds the 3 s part from 10 s in front of your request, and cuts-off the last 3 seconds. The result will be a clip in the range 10 s — 30 s.

But the situation is not so desperate. You have to force Adobe Premiere Pro to re-encode the 13 – 33 s part of original video, i.e. to first compute the frame at position 13 s, then mark it as intra-frame, and make subsequent frames dependent of this new intra-frame.

How?

As I told, I don't know the exact answer. But you have to avoid enabling properties as “Direct Copy”, “Fast Copy”, “Without Re-encoding”, etc.