The British aero-engine maker has had turbine blade problems on the Trent 1000 Package C engines - a problem that first came to light in 2016.
Turbine blades have been corroding and cracking on certain variants of the engine, prompting more frequent shop visits and a huge schedule of repairs.
Air New Zealand said the aircraft involved in Sunday's incident had a Trent 1000 TEN series engine, not the Package C engine associated with the unscheduled global maintenance requirements.
However, the Financial Times reported in June that in March Rolls-Royce revealed that intermediate pressure turbine blades on the Trent 1000 TEN could be vulnerable to the same problems, although there was no evidence any had yet been affected. It said it would replace the blades from next year.