something is definitely wrong here. I have checked this in my system using 2015.3 and CC2015 (can't tell which one of those you are using) and it works fine. exporting and importing show the exact duration/frames.
make sure your software is up to date. CC2015 should be 13.7.1 or 13.7.2 on Mac and CC2015.3 should be 13.8.1
if that does not work - I would reset my preferences: Reset After Effects Preferences.
if this still happens, try to reduce your issue and make some tests. fresh project, fresh composition, try to recreate this and see where is this starting.
You have taken a bunch of time to create a graphic but you've scaled the screenshots so much that I it's hard to read anything. My first question is did you mess with any of the settings? I've never seen this happen unless you mess with frame rates or file interpretation in AE. Your screenshots do not explain your workflow. I don't have any idea how you created the two comps with the extra frames or what the properties of the rendered video are. Check the info on the rendered video by selecting it in the Project Panel and checking the info at the top just to the right of the thumbnail. I can not reproduce your error in any way without messing with file interpretation or render settings. Try changing the Timeline display to frames, then drag an imported clip into the New Comp icon or select the imported clip in the Project Panel and select File>New Comp from selection and see if you still have the error. If your original comp has 163 frames the rendered file should show 163 frames in the info and the new comp should be 163 frames long.
You do realize that when the CTI is on the out point of any comp that the last frame still has to play so the duration of the last frame is not included in the time shown in the display. The last frame still has to play. Let's say you drop a movie that is 10 frame long in the timeline. If you select the layer and press the o key to move to the out point the CTI will show you frame number 9. This is correct because the CTI is at the start of frame 10, the last frame in the movie. If you move the CTI to frame 10 then you will not see anything because frame 10 has already played.
This is different than in a NLE like Premiere Pro. If you use the up arrow and down arrow keys to move to the last frame of any cut the program panel is blank because the CTI is parked at what will be the first frame of the next cut you put in the sequence. If the CTI parked so the last frame was visible, when you inserted the next cut it would overwrite the last frame fouling up the timing by one frame. This is normal and the way NLE's are designed.
I didn't explain my workflow as I found it to be somewhat irrelevant what I did to the clips, but here's another version. The workflow was the following, including file interpretation (not changed) etc. And the other SS were scaled as there's a 900px limit here on the forum?
New sequence of screenshots here with explanation underneath.
1. Import avi. (arena-01.avi) length: 0:00:09:19, 30 fps
2. Drag avi to "Create a new Composition" icon. (arena-02) length: 0:00:09:19, 30 fps
3. Render with default render settings and QT output module (filename: arena-02.mov) (duration 0:00:09:19)
4. Drag new QT video back into AE and check length: 0:00:09:20, 30 fps
5. Drag new video to "Create a new Composition" icon. (arena-03)
6. Observe length (see screeshot) 0:00:09:20, 30 fps
7. Blank frame at the end.
Thanks for your reply
No limit -- just a recommendation. You can paste a print screen or drag any image file into the reply field and the forum will automatically scale.
Check the real frame rates. You would get your behavior if the frame rate of the footage was 29.97 Drop Frame and you somehow got a 30 fps render no drop frame.
I'd update your version of AE, delete the preferences. There's no way to make this happen if you have not messed with the frame rates somewhere.
Thanks for sharing what caused this anomaly. I use mediainfo for getting information about my footage but nice to know VLC can do it too.