That looks like a pretty dark browny burn. But because it is all the tips, and the unaffected leaves still look firm and fine, I would say it is a burn. Fungus will often affect the stems and the leaves at the same time, and black spots can emerge starting from the area near the petiole. (And that's usually fungus killing the roots, and the plant dying as a result). I wouldn't spray fungus as long as the non-burned parts of your plant look healthy/dark green/firm.