No that's not how it works. Each Local Authority sets their own rate but only Braddan, Douglas and Onchan collect their own rates. All other Local Authorities have their rates collected by IOM Government (so only one Rate Demand - whereas Braddan, Douglas and Onchan residents get two).
The Treasury also collects their own rates and have set their rate at 555 in the pound which equates to £643.80.
Therefore a typical property in Douglas will be paying £664.68 plus £643.80 = £1,308.48.
A typical property in Onchan will pay £476.76 plus £643.80 - £1,120.56