Yes, that description is correct. I am not sure if I understand your question correctly, but the "five consecutive 3-month running mean" refers to overlapping 3-month seasons. For example, if July - September (JAS) satisfies the -0.5C ONI criterion, then the following four seasons (ASO, SON, OND, and NDJ) must also satisfy that criterion for La Nina conditions to occur. Because NOAA declared a La Nina Advisory, it means that they expect the ONI value to remain at or below -0.5C through the rest of the fall and into early winter (NDJ).