There is video which shows Bruce Arena espousing this view in the locker room prior to the 2002WC game v. Portugal. From what I can recall, what you've bolded there is an exact quote. I've always felt it is meant to convey to the players that they should seek to immediately make an impact on the field. A 'get the lads pumped up' type of mantra from a coach to help his players avoid coming out flat and reacting to the game rather than having it dictated to them. How this fits into the official's view of the match I have no idea. I'm not sure how the perceived mentality of a team would influence the way the crew calls the game.
As a referee going into what could a physical game, I keep in mind the "first tackle, first foul, first shot, first goal" philosophy, and I try to whistle that first foul, first bad tackle. In fact, I try to do it on all games, but I'm even more alert for those U16-U19 boys games.
I have always emphasized a "first 5 minutes" of each half philosophy of coaching, which I suppose is similar in principal. No problem with trying to get the first tackle, shot, and goal, but somewhat odd to see/hear that one of the "objectives" of this philosophy is to get the first foul in the game. That's a little tongue-in-cheek, as I get the principle of coming out ready to go, but if I actually thought as a ref that the foul was being committed to fulfill the coach's philosophy (as opposed to a hard tackle that simply ended up being a foul), I might be adding "first card" to the team's list of achievements. To the extent the message as a ref is that the players are going to be coming out ready to go from the first whistle, then obviously the refs should be ready as well, but seems to go without saying....
Critical periods in a game: First five minutes in each half. Last five minutes in each half. Five minutes following a goal, caution, send-off, hard foul or substitution.
I think the only thing here that would concern a referee is the "first foul" idea. I swiped Arena's little speech and use it with my HS teams when I coach. The "first foul" means to play physically and see where the level of the game is today--and find it out before the other team takes advantage to run you over. That said, I hardly see how this would make a referee do their job differently. We should always be looking for that first incident to help set the level of play. We know players will test right away us to find out where the bar is, even if they haven't gotten a speech from their coach.