What does it actually mean by the sentence "tuition is paid by the supervisor"?
Different schools, departments and supervisors approach tuition payment differently. As far as I'm aware, most universities demand that tuition get paid somehow. Some universities might not collect tuition, but given what you've posted, I surmise that your university does. Where the tuition funds come from is how it will vary.

I've seen these different approaches:


The department / school pays tuition automatically for all of its admitted students. This is rare, but it does happen sometimes. It guarantees that the student won't have to pay tuition and can focus on research that the supervisor and student decide on, without having to pursue other external funding sources for the tuition. In this case it generally wouldn't matter who your supervisor is.
The department / school pays tuition pays tuition only for the students that hold a job within the department (e.g., teacher assistant, research assistant, researcher, lecturer, etc.).
The department does not offer to pay tuition, but the supervisor already has guaranteed funding (e.g., through external grants or donations), so the supervisor has guaranteed to pay your tuition with that money. In this case, whether or not your supervisor pays your tuition depends on which supervisor you have.
Neither the department nor the supervisor offer to pay your tuition. You are expected to pay for it yourself (e.g., via student loans) or apply for external funding (e.g., grants and scholarships) yourself to be able to pay for tuition.


The sentence "tuition is paid for by the supervisor" makes me think that it is up to the supervisor's discretion whether or not they will pay your tuition (e.g., make it contingent upon whether you are making progress and / or pursuing a topic that the supervisor approves of).

In addition to tuition payments, you should also consider where your income / stipend will come from. Sometimes your stipend comes from similar money buckets like those listed above for tuition.