Well, I don't know about rollers, or naturally curly, but this site implies that the men, at least some of them, had it curled at the style shop.
A man might get his hair curled or have his hair cut. If he were experiencing severe hair loss, he might wear a wig to cover up the problem. Then, as now, some men looked for ways to conquer the hair loss problem. During the Republic, grease and oil were thought to make hair grow.
Beards were out-of-fashion among the aristocracy of the Late Republic; and didn't come back into vogue until the first century CE. So men shaved or used the pitch-and-resin-facial-hair-removal technique to ensure they remained clean-shaven. If a man were in mourning, though, his hair and beard were permitted to grow as a sign of his sorrow. The poor often ignored fashion since it was thought impossible for a man to shave himself and they could ill afford the expense of a daily barbering. Sometimes young men would wear beards just to draw reactions from their elders (sound familiar?).
As we do today, a man went to a barbershop where the barber (tonsor)--either male or female--would cut their hair or remove it.
https://en.wikipedia.org/wiki/Roman_hairstyles
