When you place your footage on a Drop Zone, Final Cut Pro synchronizes the frame you select with the first frame of the entire template (and not the beginning of the Drop Zone). Because of that, your Drop Zone videos start playing back when the template starts which results in an offset if the Drop Zone starts further into the template. If you use a really short clip, it may end before Final Cut Pro gets to display it, and the last frame will be shown as a still instead. The same will occur if you use a longer video but pick a frame too close to the end.

The workaround for Apple's "workflow" is simple: all you need to do is create a longer clip out of your short video. To do so, put your footage on the timeline and align it with the drop zone. Add any kind of placeholder (e.g. a copy of the clip or a Color Solid) and line it up with the beggining of the template. Lastly, wrap both the placeholder and the clip in a new Compound Clip (Alt+G) and apply it to the drop zone, selecting the very first frame.