The stroke on live type should be, and should only be, center-aligned. Inside and outside alignment should be unavailable. Try using the Offset Path effect to visually reposition the stroke alignment. For example, to align a 1-pt. stroke to the inside: With the type object selected, go to the Effect menu > Path > Offset Path, and enter a value of .5 pt.
If you do not require live type, go to Type > Create Outlines to adjust the stroke alignment in the Stroke panel.
Or what meganchi said.
If in fact the stroke is inside-aligned, there is something odd going on that requires further investigation.
Peter