I'm trying to answer the same basic questions as you are and have been pouring over information ever since I installed DS a month ago. What I can tell you is that this is a common issue from what I've seen in the forums and is not straightforward in exactly how to troubleshoot it. That said, the following may give you some insight as to what's happening.
First, In order to analyze it, you have to first turn on Save DeepStack Analysis in the AI settings of the Trigger Tab. This causes DS to create a record of what it used for object detection as a DAT file, that is placed in your Alerts folder. This gives you a way to review what happened. Without that, you can't really troubleshoot.
If you right click on the playback and choose Testing and Tuning, then enable Analyze with DS, that will RE-analyze the entire field of view of the BVR recording - that is the same concept as Analyze with Motion Detector, which is used to fine tune your motion detector settings; it's temporary for fine tuning, not something that's on all the time. But that won't tell you what happened when the clip was created. I'm still grappling with using DS test n tune. Just know that it's different and used differently.
Once you have Save enabled for DS, then you open the Status Window of BI from the main console and select the DS tab. When you double click on the Alert from the Clips list on the left, the DAT file will populate data into the Status window and show the analysis used. This tells you, in theory, where DS analyzed (yellow boxes in the image) for objects, when it is analyzing that area (timestamp), any object it identified at the time, and finally, the image that DS used to confirm or cancel an alert - this image is denoted by the asterisk in the object tree on the left. Side note: I have no idea how to interpret the timestamps...yet.
When there is a mismatch between the yellow rectangle and the object that triggered the camera - areas don't overlap, an alert is cancelled. Usually.
While trying to figure this out for myself, I created a video that I posted on YT here:
DeepStack Object Detection via Motion Trigger. It is just a quick visual of what I am trying to explain above. But the takeaway is...
BI drives what area will be used by DS (yellow rectangles) for object identification.
Page 70 of the help file says: "You may also benefit from configuring the motion sensor to use more sensitive settings so that more events will be evaluated by the AI. This is done by lowering the object size and contrast, as well as possibly reverting to the “simple” detection algorithm."
So in summary, first turn on the Save dat part. Then review your cancelled alerts to see what area is being analyzed for motion and what DS identifies. The tricky part is figuring out what to change and where.
There's more to it, but that is how to start trying to figure out what's going on.
Disclaimer: The above are my conclusions from my own research and as such, I could be wrong about some things. There is a notion that the best way to learn about something is to try and explain it to someone else - that's pretty much what's going on here.