This makes sense
It doesn't look like Mars has had plate tectonics since a very early phase in its evolution, so since then, the lithosphere has remained effectively stationary over the Mantle. Plumes would continue to feed partial melting under the same point in the surface allowing volcanoes to grow and grow. Here on Earth, the movement of the plates means that plumes leave traces on the surface (such as the Hawaiian islands and Emperor seamounts in the Pacific) so volcanoes can't grow too large before they drift away from the plume head and become extinct.
We also know from plumes here on Good Old Earth that they are amazingly long lived. The Reunion Plume is at least 66 million years old (when it created the immense Deccan Traps and did the hard work of killing the dinosaurs), that under Kerguelen is in excess of 120My. Even if it was only supplying a fraction of a cubic kilometre of magma every year, that would allow for some massive volcanoes to grow on Mars.