The reason for the @ prefix is that sometimes the bot is doing kicks or bans or giving status that only an OP can do. But in this case it doesn't look like any of these triggers are doing that.
It's probably a good idea to figure out how to give your bot status, to lessen the chance of a trickster imitating your bot by changing their nick to be similar, like changing the one into a small L and becoming aribun2l
