just curious because I know only Commmon Bro-Mon spawn in that box.
Nothing will happen!
Ok, so as you said that you think that only Common bro-mons will spawn in that website? Sadly that’s not true, every bro-mon spawn place is random, it’s not setted to only appear on one website only
So after you caught all common bro-mon, you won’t see them 
until the next update if it contains Common bro-mon
Now go to the main question, after caught all common bro-mon, what will happen?..Other Crush(Level, Rarity) will appear instead of only Common