As a steward at Old Trafford for the past 4 years, and a steward at Wigan for the past 3, i can't say i know of any choreographed movement during the game at any stadia. I can't even think of any reason why you would have noticed it. I suspect you aren't actually talking about the stewards, and perhaps you are talking about the outside security team 'CES' (Controlled event solutions).
At each stadium, you have safety stewards who operate inside the stadium, away from the pitch. Crowd / General stewards who are supposed to stand with their backs to the game, facing the crowd to spot any infringements, potential hazards or trouble makers (though the majority stand there watching the game). And you also have an outside security team, charged with searching fans entering the ground and throwing out any persistant trouble makers. These are usually ex-forces or part time doormen. Either way, stewards wear bright orange jackets and CES wear bright yellow.
I suspect its the security team that you have spotted moving up and down the stadium, this may be part of some tactic they employ when they are understaffed, to ensure all areas of the crowd are covered. Thats just a guess though, i could be wrong.