Yes, obviously the number of products to be displayed was set >3 and sure to 20 as the pagination shows that.
I guess it means digging deeper into why only 3 products show. Even if you're ok with it for now, I'd think you'd want to have control over how many are being displayed, but in fact, presently you seem to not have that control.
BTW, you've set the number of items to 20, but what did you set the number of columns to? Could it be that it's 3?
I haven't managed to find that section on your site yet, but my best next guess is that there's a factor in the site template which prevents from seeing more. Obviously, it's not a responsive one. Should still work because HikaShop was well around before everything became responsive, and it should still work. 
Oh, and a compliment: cool stuff, those Tünnis! I want one!!!!!