Preserving Frame Rate
At first I did not understand your question, after you have supplied the example video I understood what your problem is.
The issue is that when you import the Images, Premiere Pro assigns a default Frame Rate to them, which might be different from what you desire.
Changing Sequence Frame Rate does not change Images default Frame Rate when you import them, to fix this you can do the following:


Create a new Project
In Project Window right click > import > select first Image only and check Image Sequence.

Right click on Image Sequence in Project Window > modify > interpret Footage.

check "Assume this frame rate" and set desired FPS and click OK.

Drag Image Sequence from Project Window to Timeline. Then Render/Export as usual and make sure the Frame Rate at export matches the one you set up earlier.


NOTE: Image Sequence imported, Sequence in Timeline and Export Settings have to have the same Frame Rate.
That is all. You should not have any Skipped or Extra Frames in output video.