My friend owned the Genie version and I did sew a project with it many years ago. It was a nice machine.
First I would bring the bobbins and machine back to the shop to try to resolve the problem. The no brand bobbins "might" be the problem.
That being said I don't think it would matter if the bobbin was a no brand or Singer. There may be a slight difference in specs of the new bobbin that is not noticeable to the naked eye. This may be no problem for the modern machine but it seems to be for vintage and antiques machines. I too had the same problem as you when I tried a new Singer brand bobbin in my 66 treadle. It works fine with the old bobbins. Since I have several old bobbins I didn't mess around with tension to try to resolve the problem.