The default generating rules in the screening platform provide the minimum aberration design. As you've noted, changing the boxes changes the design, and changes the "defining relation" that determines which effects are aliased. The default minimum aberration tries to minimize aliasing of the lower-order effects as much as possible.
Some design of experiments textbooks and papers provide tables of design generators that lead to designs with certain properties. Minimum aberration is a good general rule of thumb, but there are certainly other possibilities, such as maximizing the number of clear effects. If you are looking to estimate particular effects, I would suggest trying the Custom Designer rather than the Screening Design platform.
While there's not much information in the documentation, if you do an online search for "Defining Relation" and "Design Generators" you should find sufficient information. I will put forward a suggestion to the documentation team to provide more details in a future version of the documentation.
Hope that helps!