Just played through the tutorial on this, myself. My understanding is that it has to do with the gauge on the left side of the screen. Each time it fills to the point where it's at the limit for that "level" of the gauge, then you'll need to do one of those R2 team-attacks to push it up to the next. Rinse, repeat. Once the gauge is filled to the tippy-top, doing a team attack will push you both into a sort of overdrive mode where you temporarily have no limit on your combos or TP attacks.
That person isn't talking about those, they're talking about the unique team normal attacks (not an arte) that sometimes happen. Not sure what triggers it exactly.