Nope, there shouldn't be any red tint to the gray scale patterns. I doubt if you've "messed up" your grayscale, since with a noticeable red tint it was FUBAR to begin with, but you can definitely adjust by eye for best-looking gray. To get to the recommended D65, you do need some form of instrumentation or an optical comparator. Just be aware that the cuts and drives actually have an effect on both ends of the gray scale. On my Mitsubishi CRT RPTV, for example, lowering a color's cut boosts its drive. On other makes, lowering a cut may lower the corresponding drive. Using AVIA's crossed-step scale or crossed-ramp patterns can help you see what's happening as you make changes. AVIA's grayscale patterns are known to have a tiny amount of magenta tint in the darker grays, but this shouldn't be visible. I do recommend you make these adjustments with the room as dark as possible, as other light sources or colors around the set can affect your color perception and thus your results.
Oh, BTW, if you're feeding your display via component from your DVD player, you can get a pure black-and-white signal and knock out the magenta contamination by disconnecting the red and blue component cables. Some displays (I don't remember which right now) don't act as you'd expect when color is decreased and actually make grayscale patterns appear tinted when this is done. One maker's sets glow a bright Kryptonite green when color is reduced to 0!