Does the UK visa work on the Isle of Man?
You don't need a separate visa if you already have a valid UK visa.
If you already hold a valid visit visa for the UK, you do not need to apply for a separate visa to visit the Isle of Man at the same time.
And here is some context to understand why is that the case:
The Isle of Man is an internally self-governing dependency of the British Crown; Her Majesty Queen Elizabeth II is the Head of State. As a British Crown Dependency, the Isle of Man is entitled to, and uses the services of the British Embassies and other diplomatic offices around the world. One of the services provided by the British Embassies is to act as agents in terms of handling initial visa applications submitted for the Isle of Man.
Isle of Man, the United Kingdom, the Channel Islands (Bailiwick of Guernsey/Bailiwick of Jersey) and the Republic of Ireland collectively form a common travel area (CTA). This means that an applicant who has entered the common travel area and who has been examined for the purpose of immigration control (for example in the UK) does not require leave to enter any other part of the common travel area. Simply, travel between the Isle of Man and the United Kingdom is an internal domestic journey and there is no separate immigration or other control.
However certain persons subject to the Immigration (Control of Entry Through the Republic of Ireland) Order 2016 who enter the Isle of Man through the Republic of Ireland do require leave to enter and should report to the Isle of Man Immigration Service upon arrival in the Island to have their visa issued.