You know, in a funny way the "Yemeni admixed" assumption isn't 100% false:
Somalis do actually seem to descend from Yemenis through Highland Ethiopian admixture but it's obviously Iron-Age admixture. Then there's the fact that the
absolutely prolific Camel clearly seems to have come Yemen given archaeological and linguistic evidence, as did our second most common Y-DNA lineage (T-L208), our religion (same school as in Yemen), iron based metallurgy, asiatic admixture in our non-camel livestock, our adoption of the Arabic script and possibly Musnad based scripts before that... the list goes on.
The imagery of Yemenis coming down to the Somali coast or the whole Horn and affecting it isn't an incorrect one; the extent to which—ancestrally—is simply exaggerated and most of our MENA roots predate that and come from what is now Sudan and Southern Egypt.
Yemen is in many ways the ancient Greece to the Horn's Rome. I think that analogy actually quite fits as the Horn in many ways, and at certain points, did eventually surpass its "teacher" from the Habeshas once ruling chunks of southern Yemen during antiquity to Somalia becoming its bread basket, and becoming so economically indispensable to cities like Aden during the Early Modern era that the British feared the city would be donezo if the Somali population left as they were threatening to do at one point.