You are correct about setting the Solder mask minimum width to 0. If it is non-zero, KiCAD 5.1.2 makes polygons from touching features like this.
If you set the minimum width to 0, you get “flashed pads” with tool codes. like this:
I will be setting minimum width to 0 for all my future work.
Why would you want this? @Rene_Poschl has some strong opinions about it which I understand but the board house must have flexibility to adjust things to make the result come out the way that you want. They cannot adjust a polygon margin but they can adjust the flashed pads in order that the result is exactly what you requested.
@Rene_Poschl : another point to consider is that when you specify a 10mil drill, they don’t use a 10mil drill bit. Rather, they calculate how much copper will build up in the via, add that to the diameter of the drill bit, make the hole oversized, plate the board and fill in the vias, ending with a finished hole size that is the diameter that you requested. These types of adjustments are made all the time in order to satisfy the customer. I think they use domain-specific knowledge that most of us don’t know or care about in order to get as close to what we want as possible. I’m content with that and don’t consider it a breach of contract. I hope this helps.