My understanding of this feature of Shotcut is that it allows us to combine videos of different resolutions and framerates, and have them work nicely together.
I think of the Video Mode as the “canvas” on which videos are applied.
Example: you have a 30fps and 60fps video that you want to combine into one 30fps video. Open the 30fps video, which will set the Video Mode to 30fps. Now when you add the 60fps video, it will assume that you want it to ultimately play in 30fps, and rather than matching frame-for-frame, the 60fps video effectively becomes a 30fps video. If you were to then change the Video Mode to 60fps, I believe what happens is that it takes the same 30 frames that were on the 30fps canvas, and stretches them out to fill the larger 60-frame canvas, so your project is now half as long (time-wise) as it was before, and plays at twice the speed.
If you set your Video Mode in advance, everything works well, and it IS working the way it’s intended… that said, it would be a neat feature to have a “Reset Video Mode” option, or something like that, that re-interprets the clips in a project maintaining time rather than frames. It looks like something similar was just added in regards to Keyframes in 18.07 (“Keyframes are now saved in the project file using time clock values instead of frame numbers to make them adaptive to frame rate”) so maybe it will happen someday.