What are the tectonic implications of the Quaternary Igwisi Hills, Tanzania, kimberlite volcanics?
The Igwisi Hills kimberlites erupted through the Archaean aged Tanzanian Craton, which resides in between the eastern and western branches of the East Africa Rift (1), in the vicinity of the Gregory Rift (2). It is a series of 3 volcanoes, evidence has shown that these eruptions were the result small volume monogenetic eruptions (3).

Seismic studies and observations detected that the cratonic lithosphere base is approximately 170km, after which, there is anomalously low velocities to a depth of about 350km (1), which according to models described by Weeraratne et al. (1) indicate that beneath the cratonic crust, there is the presence of high temperature and the presence of melt:


a transition to a younger 'more fertile' asthenosphere.
crucially in terms of the local tectonics, indicate the presence of a mantle plume head causing the craton to experience uplift.


The mineralogy of xenoliths in the pyroclasts and lava further indicate that there has been small degrees of carbonate-apatite bearing peridotite source melts from depths greater than 110km. (2)

Brown et al. (3) conclude that the fact that these kimberlitic volcanics are so comparatively young, they may indicate that a new phase of kimberlite activity may be starting in the Tanzanaian craton, especially when considering the mantle plume and active rifting in the adjacent East Africa Rift branches.  This suggests that a link between kimberlite volcanism and the supercontinent cycle maybe too much of a simplistic view, when the reality is probably closer to individual plate reorganisation (in this case, the eventual splitting of the African continent). 

References

(1) Weeraratne et al. 2003, Evidence for an upper mantle plume beneath the Tanzanian craton from Rayleigh wave tomography, Journal and Geophysical Research.

(2) Dawson, 1994, Quaternary kimberlitic volcanism on the Tanzania Craton, Contributions to Mineralogy and Petrology (abstract only - paywalled)

(3) Brown et al. 2012, Eruption of kimberlite magmas: physical volcanology, geomorphology and age of the youngest kimberlitic volcanoes known on earth (the Upper Pleistocene/Holocene Igwisi Hills volcanoes, Tanzania), Explore Bristol Research (abstract only - paywalled)