Yes, with a red arrow, the player will act as the position ahead of when attacking, and his own position when defending.
DR with red arrows = DMR on attack and DR when defending.
With blue arrows, DMC = DC when defending, DMC when attacking.

Strikers don't need red arrows.
Defenders and goalkeepers don't need blue arrows.

I usually only put red arrows if you are attacking on that side.
Attacking down the wings = red arrows on wide players, from DL to AML, DR to AMR.
Attacking through the middle = red arrows on central players, AMC and maybe MCs.
You'll need to balance it with some blue arrows elsewhere, though.