Arrows are not a mystery. Imo, the game, as with many games, uses a less > average > more mechanic.
When you set the formation in a the grid an arrow does not move a player forward or back a box. That's bogus imo. The grid is just a graphical representation of relative positions and a means for the game to check and apply 'factors'.
Attacking Mentality makes a team more attacking and Defensive mentality = more defensive. Arrows do that to an individual player.
Ask yourself what Attacking does at a team level and that's what happens at a player level.
Red arrows = Players will get forward more and use Attacking skills more.
Blue Arrows = Players try to fall back more and use Defensive skills more.
On topic, differing stategies will depend on the level of activity of other managers. Generally speaking, at low levels attacking is the best poilcy but against an experienced manager this could unravel.