An image may appear to be fixed by the red eye tool even though there's still some red visible under the loupe or in a print.
This can happen whenever your image is scaled to fit your screen or Viewer size (which is most of the time), as opposed to being zoomed to 100 percent. Image scaling can obscure some smaller details.
Therefore you should check your work by using the loupe or toggling to 100 percent (Z key) before concluding that it's fixed.
Tip: This is also a good idea for checking noise reduction, spot & patch, and sharpening adjustments.