Refresh my memory, people. If I have a critter with supernatural abilities (save DC = 10 + 1/2HD + ability mod), and I give it class levels, do the save DCs increase?
Well, the formula would certainly apply if you just gave it more creature HD, but I'm talking about class levels here. IIRC Savage Species said something about how class levels don't count, but I could be wrong.
Well, if you are pointing at the associated/nonassociated class levels as described in the MM page 294 than I would say this rule doesn't apply because it refers only to CR.
But maybe this sentence from the MM (p. 290) may help you
When a monster adds a class level, that level usually represents an increase in experience and learned skills and capabilities.
As a related note, if you gain a supernatural ability (i.e. through a spell or feat), it usually states, that the DC for the ability is calculated according your total hit dice (class levels).