My Tilix/zsh combination just pastes the content as a multi-line entry to the terminal. If the clipboard contains control codes (e.g. arrow up) they are entered verbatim (as if I had used the quoting function ^V to enter them).
So I suppose we're not very far from this not being a problem in general.
Though I understand this also works via control codes. I hope Tilix is smart enough to filter them out from the clipboard before doing this..
edit: I tested that case out, and it works. I suppose the protocol uses quoting.