Firm tofu is basically just soft tofu that's been pressed and drained. If you went out and bought soft silken tofu then you could probably just mash it straight into your sauce; extra firm tofu is harder to mash simply because it has a much lower water content. But as Michael says, you could still do it, it would just be a little more "crumbly".
I'm not really sure that there's any interesting or sophisticated chemical reaction going on here; you're just getting it wet, and being wet makes it softer and easier to mash up. It's more or less the same thing that happens with pasta, except that tofu doesn't contain any starch and probably doesn't need the high temperatures, so I doubt you need boiling water for this; just soaking it would give you the same result and wouldn't hurt the flavour as much as boiling.