Sure, Carlo beat Connie because he just was a scumbag. At least, that was the only reason in the beginning. He beat her, Sonny saw her, and then PUBLICLY lost his famous temper when he beat Carlo in the street. That was how Barzini knew that if Carlo did it again, Sonny would again fly into a rage and leave the compound and his bodyguards.

The day of Sonny's death, Barzini's people made SURE that Connie would start a fight with Carlo. They had the girl call his house, Carlo made her cook and then refused to eat, causing her to break all the dishes, etc. and start a fight with him. Then, after Carlo beat her, he made sure that she had the opportunity to contact the compound. That's how they knew.