Probably due to apical dominance!
In certain plants the very top bud on the stem produces auxin which inhibits the other side shoots from developing, e.g. chrysanthemum.
So if you "stop" the plant by removing that top bud, the auxin stops flowing and the side-shoots can develop.
When the Kafir lime part of the plant died, there was now more auxin being produced, so the shoots further down, i.e. the rootstock could start to shoot.
That is the general drift, Uni was over 40 years ago!