I got a flat with my Mini from the liner where I cut it shorter.
The end's edge was sharp, and I have now used tape over the sharp edge to protect the tube.
I've had similar problems when I have cut the liners with sharp square corners. Cutting rounded corners helps, and I have tried sanding the edge to smooth it.
I think tape plus rounded corners would be easier. I always seem to have short spare pieces of cloth rim tape about. Now I know what I can do with it!