What concerns me still is the timing of Holgate's reaction. I have not studied the incident, but I hear the suggestion that Holgate appeared calm while Firmino called him "filho de puta" but reacted strongly to something after that - when Firmino's mouth was not clearly visible behind Kenny's head. My concerns are lessened by the fact that the referee ... and other players .... showed no sign that anything significant was said.
N***** isn't a Portuguese word (nor is there an equivalent word) so it makes no sense that he throws that word out there. I think the slight delay was because it took Holgate that second to figure he had an opportunity to sling some mud and avoid getting sent off. It was a lightbulb moment.