There is a comment elsewhere from the creator I think that explains this. The 5th "a" never gets added, you'll see that the cells turn red. After you remove 4 "a"s then you're back at 0 and it is correctly reporting that there aren't any.
Re multisets, yes cuckoo filters and counting blooms are bounded - cuckoos by entries or bucket x 2, and blooms by bits per counter. Cuckoo's counting capability is more a side effect of the design. It's really only interesting in that you get limited counting in roughly the same bit space as a non-counting bloom. I suppose you could add counting bits to a cuckoo to support higher bounds in a similar manner to counting blooms.
I'm curious to hear more on your point on K-hashing in bloom filters - would you expand on your statement about only needing a K-bit hashing function? I'm happy to update the text on the tutorial to be more clear/exact.