The Referee is the decision-maker in any match, and has ultimate responsibility for all that happens. Think of the Referee as the manager, and the Marker as his/her secretary.
The Marker should introduce the match, call the score, call the play (out, down, etc.), announce the state of the match at the end and beginning of each game, and repeat the Referee’s decisions after appeals. The Marker should concentrate on only watching the ball so that he/she has a better chance of calling the rallies correctly.
The Referee is in charge of all other things including court conditions, player clothing, all timings, conduct on and off the court, injury/blood decisions, ruling on all appeals made by the players, and can over-rule a decision of the Marker at any time.
Both the Referee and the Marker should keep a record of the game (score sheet), and in any disagreement, the Referee’s score sheet is the one that will count.
Note that rule 3.7 says that the Referee’s decision is final, that is, there is no appeal against the decision of the Referee. Nor is there any appeal against the Referee assigned to a match!