Transitions "not working?"

If you want a crossfade between clips, you need a few extra frames at the end of the first one and the beginning of the second one.

These frames are then used to create the fade effect.

 

You need to re-think how you visualize transitions.

When you are adding a transition, it is blending footage from the first clip into the second. Thus it isn't starting at the beginning of your second clip - instead it is using footage prior to the beginning of your edit so it ends at that point. If you are adding a 1 second crossfade, for instance, it is starting 15 frames earlier than the end of the clip (and likewise, it is continuing 15 frames AFTER the end of the clip preceding it). Thus you need excess footage before and after each clip in order to implement transitions.