I do only portraits and retouch the negative first and then the print. The dye retouching is far more extensive than just spotting. If there is a lot to do I often do it before I mount the print because you can wash it off if you screw up.
More often than not though, I do it after the print is mounted because it is easier to work with a flat drymounted print.
I've never seen a color change from the heat of the press.
The dyes I use are Veronica Cass.www.veronicacass.com