I think the problem is not with aligning the actual text. This seems to work ok, at least it does when I try it. Text with multiple lines wiill align left, center or right when using setAlignHoriz() method, even on its own without the calls to update methods. I think the problem you are having is with sizing and wrap widths. The lines will be written and their text can be aligned correctly, but they are always positioned so that the center of the text box is at your desired location. Alignment does not change this, it changes the alignment within the text box. If the wrap width is not stated, it will look center aligned regardless of your text alignment in the box, because the text box is made to fit the text.
Try changing your wrap width of your text objects so they are all the same. So, I think you are using height units. Try .3 as a wrap width. Then, try moving your text closer to the scales on the x-position axis, and aligning your text left.