When you place your footage in 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). As a result, your Drop Zone video playback starts at the very same moment the template playback starts. The further into the template Drop Zone starts - the bigger the time offset in your drop zone clip. If you use a really short clip, it may even end before Final Cut Pro gets to display it, and its 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 beginning 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.
Check also: Old/Alternative workaround