This summary is not the rule. The rule text controls.
City courts outside New York City can offer arbitration as a way to settle a case without a full trial. If the Chief Administrator of the Courts has set up this arbitration program in a particular court, the case will follow the statewide rules found in Part 28 of the Rules of the Chief Judge. Those rules spell out how the arbitration process works from start to finish.
If both sides in a case agree to arbitrate their dispute under a specific law called UCCA 206, then a different set of rules applies. In that situation, the arbitration follows Article 75 of the CPLR, which is the general state law covering arbitration procedures. So the rules that apply depend on whether the court has its own formal arbitration program or whether the parties simply agreed on their own to arbitrate.