Intermixing Greco-Romans with potential ranges of intermediate genetic profile (Cypriot-looking) likely mediated non-local elements. The bi-directionality is never symmetrical. For example, those Greco-Romans already carried Levantine ancestry, combined with their Southern European DNA, might present new phenotypes during the re-introduction of said Levantine influence.
Such types of mixing were channeled through religious and civilizational coherence. Later, I imagine most of these intermediaries were phased out by the genetic convulsion of the broader reorganization of the region.
In that sense, you can have minor actual Southern European genetics but with considerable change in phenotype arrangements because of how sections of those genetics were sent back by people who reworked the genes with other foreign ones, representing unique/novel phenotype signatures, irrespective of the majority Levantine-looking DNA structure on the surface on admixture perspective. Possibilities for phenotype frequency retention are possible, even in the conditions where Levantine ancestry overturns those descendants of mixed peoples to almost unnoticeable proportions.
You then have conditions such as selective sweeps that can disproportionally influence the propagation of alleles regardless of negligible mixture levels. Non-predictable genetic complexity in a differential population influence can have a wide impact on things, even if the result is a relatively homogenous regionalization.
Reflecting complex mixture mechanisms with genetic stochasticity, complex assortments on several levels, phenotypes known specifically to have a strong association with a specific ancestry background can become decoupled from that correlation, demonstrating a non-associative influence that does not align with the ancestry proportions of the ancestry the phenotype originally was associated with.
These blond kids could have less foreign autosomal influences than people who look much darker than them, in theory.
Phenotypes and genotypes are not always strongly fixed together; they can have separate natures. The eventual decoupling nature of phenotypes from source populations' genetic influence in admixture contexts might not be predictive of stronger autosomal presence by the initial introductory source population by a given trait originally associated with that source population.
A trait associated with a specific source ancestry background can be decoupled eventually. So that trait might not be predictive of elevated autosomal prescene at all.
Also, as previously stated, in this specific case, it could have aligned itself to the back-introduction of the majority Levantine pulse too, given that mixing was probably done by these already highly mixed peoples that already were considerably Levantine but had Greco-Roman culture (Anatolians). People of that region in those specific times were less genetically fixated than what culture you presented. To reiterate, you had a clear flux of regional peopling of northern Levantine peoples of the broader region that sort of removed whatever variation existed on the autosomal side of genetic complex substructures outside the normal, matching a regionalized genetic continuum. Because of the factors above, the traits could have been retained in certain frequencies despite this overturn.
In one thread, you had someone asking about the occurrence of coloured eyes in Somalis and half-Somalis and this one. You have a fixation with outliers. Sometimes, I wonder why you ask these sorts of questions. This isn't Quora. 
