You did not share the formula that you used, but if you made your calculations as if they carpets were one year old (based on when they moved in) as opposed to four years old (based on when they moved out) then you miscalculated. Your figures imply that carpets in a rental unit can last 15 - 20 years, and that's not realistic.
It should not be a surprise to anybody who knows about cats, and even less to a professional carpet cleaner, that unless promptly, fully and properly cleaned up (e.g, with a product like OdorMute) cat urine penetrating a carpet into the pad is likely to necessitate replacement of both the carpet and pad.
At this point you have not shared any facts that would support their counter-claim for cleaning services, nor for pest control they obtained on their own initiative without any indication of either need or notice to you.

