Someone is probably self-employed and shouldn’t be paid through PAYE if most of the following are true:
they’re in business for themselves, are responsible for the success or failure of their business and can make a loss or a profit
they can decide what work they do and when, where or how to do it
they can hire someone else to do the work
they’re responsible for fixing any unsatisfactory work in their own time
their employer agrees a fixed price for their work - it doesn’t depend on how long the job takes to finish
they use their own money to buy business assets, cover running costs, and provide tools and equipment for their work
they can work for more than one client