This is remarkably easy to explain in terms of the current state of knowledge of island arcs & backarc basins.

In the start of a cycle there is a Rebound/long duration mercalli X (r/lx) earthquake which relaxes the overriding plate and lurches the descending plate down the trench. The crustal relaxation opens subparallel fractures in the overriding plate (in this case the NZ part of the Tonga-NZ backarc basin. The last event @ NZ was the legendary "Hao Whenua" event of about 1460AD. The result of which was a large earthquake & a bloody great big tsunami.
The subparallel fractures aligned perpendicular to the vector of the runout incorporates magma from discs accumulated under the tight crust of the formerly compressed overriding plate which then seal as the relaxing crust pinches out the base of the fracture in listric bookshelf faults.
The result is a dike of fresh magma @ the base of the crust which then transfers along the strike of the dike as the crust recompresses. In NZ the recompression vector is NE-SW or thereabouts and the fastest rate is in the NE. part of the arc at the approx. location of "Brothers" volcano and decreasing S. which transfers the magma in fractures to the S. with time along the strike of the fracture set (runout vector was either E. or ESE.).
The interesting bit is that thanks to the convergence rate, r/lx at NZ may transfer magma from the Tonga & Kermadec backarc basins into the NZ backarc basin @ a point where the NZ arc relaxes after Tonga & Kermadec with the result that magma may travel huge distances from the source. and be VERY gas rich when arriving @ NZ producing huge volcanic eruptions in the TVZ where the backarc rift intersects the arc graben and magma input long term has partially melted the crust.

Rangitoto appears to be a volcano of the backarc backfault area and appears to have been active in short term eruptions prior to the Hao Whenua event. This magma appears to have arrived from Kermadec or thereabouts and erupted @ Rangitoto because the fracture struck the backarc backfault & could go no further. The big eruptions @ Rangitoto occurred AFTER the Hao Whenua event when the crust @ the Auckland field had relaxed, and recompression beginning further N. squeezed in the remaining part of the magma filled fracture.

This activity is VERY common in classical island arcs and builds conical stratovolcanoes around a central vent over a long period of time. Ngaruhioe cone is a typical example. The reason why it is unusual in most cases in backarc basins is because of the timespan between eruptions which means that in most cases a backarc volcano's upper plumbing is cold rock and a new rising dike vent needs to be forced into the field before magma can erupt, which scatters vents over a wide area. In the case of Rangitoto, the magma filled feeder fracture @ the base of the crust was bigger than average and took longer to squeeze flat than average resulting in an eruption chain.

Have a nice day: Ag