This is fairly typical behavior. In general, any video player (except iOS) is going to recognize your video as 120 fps, and will play it back at normal speed. If the video player has the capability to play at 1/2x or 1/4x, you can do that.
But, before your video player will play it like you see on your iDevice, where a portion plays slowly, and the rest plays at normal speed, iOS needs to "bake in" those different frame rates. I think iOS will do this during the process of posting videos to YouTube, etc. But, in this process, I think it strips out 3 of every 4 frames of the normal speed part, and sets it all to 30 fps.
If you download iMovie, you can do your own "baking", and even set multiple segments to slow motion instead of just one, all while keeping your original file intact.