rnr, if you're holding the guitar on a strap, does the headstock bow out, AWAY from your body, or curve back, TOWARDS it?
If its bowing away from your body, which you seem to describe at first, you need to loosen the rod. The truss rod's function is to apply opposite force than the strings, so tightening it pulls the neck back in, towards the left side of your body, counteracting the string force, which pulls the headstock forward and away from your body.
In the picture below, the following conditions are the case:
1 - Truss rod too loose.
2 - Potentially correct setup, depending on the guitar. (A lot of guitars require just a little bit of forward bow, to get the best action throughout the neck)
3 - Potentially correct setup (Potential for buzzing, unless fretwork is PERFECT)
4 - Truss rod too tight.
Hope this helps.