A cross transition works by overlaying one continuous clip with another. The random footage you are seeing in the cross transition is actually footage from the clip
after the transition that comes before your clip cut.
For example, if your two clips are set up like below, with the cut in the middle:
=Footage A===== | =====Footage B=
The cross transition (the top line) would actually look like this:
|=Before=B============After=A=| Cross Transition Effect Bar
=Footage A===== | =====Footage B=
In order to make your cross transition work right, you have to make your cross transition cover only ONE clip, like this (if you want to cross the unseen part before clip B onto A before showing clip B, and ignore the starred areas -- those are for formatting):
|=Before=B=====|**************** Cross Transition Effect Bar
=Footage A===== | =====Footage B=
Or like this (if you want to cross the rest of clip A onto the start of clip B):
****************|======After=A=| Cross Transition Effect Bar
=Footage A===== | =====Footage B=
Try this out in your Premiere and see if this helps with your transitioning issue.
