If something happens irritatingly, it keeps rubbing you the wrong way. An irritating habit, a delay, a little noise, even a person being right at the wrong moment — the adverb sits on the thing that causes the annoyance, not on the annoyed person's temper. He was irritatingly calm means the calm itself got on your nerves. The word often carries a slightly weary, almost amused complaint, though it can be sharper. It is common in everyday English. Though actually, learners mix it with irritably: one is the mosquito; the other is how you slap. Put irritatingly on the cause.