My question is: If I use one of the domain abilities, in this case touch of chaos from the chaos domain, does the person who is touched notice that I am the source of his bad luck next round?
Only if they succeed on a spellcraft check.
They would know they have been affected by something the moment they take their save (pass or fail, they still know something hit them and they'll know if they made or failed the save), though they don't necessarily know what or by whom. Of course, since you're touching them right at that moment, it should be pretty easy to figure it out.