Yes, the telephone hearing is legal and is the most important part of trying to obtain unemployment benefits when your former employer protests.
The person running the telephone appeal is an administrative law judge, sometimes called a referee. That person has the power of a judge whom you see in a regular courtroom. The evidence and testimony that is presented at this telephone hearing should be your entire case, just as if you went to court in person.
Anything not presented or not said at this hearing will be barred.