I'm not familiar with that program, but the first time I used Drone Deploy it did the same thing. With DD you need to change the map name to get it to save a new map, it doesn't have a Save As in the directory.
The app does not prompt for a file name. It does save each entry as a project (Project 0024 in the above image). It will overwrite files if you don't have room on your iPad. The only way to clean your iPad is to wipe it and start new. Serious design flaw in both products, but it is what it is. I do not fly many repeats so I don't save missions (for the Inspire)
Try resetting the mission shape and location each time you create a new project. I always back out to the mission type selection menu and then reset the mission location for each new project. I’ve found that avoids saving over projects as you’ve described (on iOS at least).