Your problem is very similar (not exactly same) to one asked in this question. The answer to this is though same.
You cannot utilize any standard component to interact with any of your custom component. In your scenario, you are using the standard "Files" related list, so there's no way capture any event from that to be able to utilize it in your custom component.
The only way I find you may be able to refresh your component with the uploaded file is to keep on "polling" or "refreshing" your component at regular intervals, but this can be an overhead at times.
The other option was, if you had implemented the file upload feature in a custom way using lighting:fileUpload, you could have used the
onuploadfinished. With that you could have raised an event with every upload, so that your other component handles that and refreshes the data every time you upload a file.