Should I use my primary hand to do eighth note hats?

Before you start thinking I’m cool, I’ve decided to steal my niece and nephew’s copy of Rock Band 2 and teach myself some rudimentary drum skills.

One thing I was confused about when I was learning different beats was which hand I’m supposed to use to do eighth note hats when I’m doing a standard rock kick-hat-snare beat. I seem to remember the drummer in the band I was in crossing his hands while he played (playing snare with his right hand).

My kit is reversed for a left-hander (snare farthest to the right).