How to handle text nodes that contain text that goes below baseline?

There's a property for nodes: text depth

One can simply set it to 0pt for the offending (or all) nodes.

Note

Of course this is well documented in the pgfmanual.

This is more of a pointer (can't get TikZ at the moment), but since you are not getting anything else, there are two things to try:

1) There is the $\smash[b]{\text{my text y}}$ (you need amsmath for this).

2) Maybe \raisebox{0pt}[0pt]{my text y} is what you want.