It depends on the legislation that sets up the tribunal
Tribunals are government or private decision makers and they must act within and adhere to the powers given to them by Parliament. Just like a Minister of the Crown, or the clerk at the motor registry must.
Unlike a court, a tribunal must follow the law they are given. A court can decide what the law is.
Therefore, it’s impossible to say, in general, what discretion tribunals have with respect to their procedures. If a specific procedure is mandated by statute, they have no discretion: a decision made that doesn’t follow that procedure is void. Or the legislation may give the tribunal wide discretion about the procedure.
For example, consider adjudication and arbitration. Both are legislatively authorised private dispute resolution mechanisms where the decision maker acts quasi-judicially.
An adjudicator has no discretion to vary the strict timeframes in the legislation and must consider only the things the legislation tells them to consider and must not consider anything else. If they stray outside those parameters, the decision is void.
An arbitrator must decide the dispute using the procedures the parties have chosen, either in their arbitration agreement or during the arbitration. If they can’t agree the procedure, then the arbitrator is empowered to decide on the procedure. Similar decisions are available about whether and to what extent rules of evidence will be followed. Usually this involves adopting the rules of an arbitration association but if the parties agree the dispute will be resolved by the arbitrator tossing a coin, the legislation allows this.