Have you tried to put 2 fresh primers in your seating tool and seating the top one? One on top of the other.
Does that reproduce the shape of the seated primer in the photos. The extra primer will probably stay in your primer seating tool/station. Don't know what brand of press you are using, but with some models I have, the above would be possible.
What does the shape of your primer seating tool look like. The primer should be flat when seated. Not sure why the bulge is there. Even if the primer seating tool is concave, the primer should be mostly flat when seated because the press fit is on the OD of the primer.