The barrio that you are referring to is located in the western edge of the city, in an area called Tlailotlacan. It was first identified during Rene Millon’s survey based on high quantities of surface ceramics that reassembled those of the Zapotec Capital of Monte Alban (primarily graywares). In terms of why people have connected to the valley of Oaxaca (problems of identity in archaeology aside), there are mainly two lines of evidence, ceramic artifacts and burial practices.
Excavation by John Paddock and Evelyn Rattray yield high number of Zapotec looking ceramics. What makes them Zapotec looking? They mostly have medium to dark gray surfaces, indicating that they were manufactured in a reduce atmosphere (common at the valley of Oaxaca), while most of the Teotihuacan ceramics (like the Thin Orange wares) tend to have lighter colors, indicative of their firing in the open air. Rattray even found what appeared to be unfired ceramics and rejects made or decorated on Zapotec styles. It is interesting to note that while the majority of the ceramics were made in Zapotec styles, they were made from local clays. Very little of the ceramics were actually imported directly from Oaxaca. Censers, and other ritual objects were also done in Zapotec canons, rather than Teotihuacan ones, to the point that sometimes it is hard to differentiate between imports and those locally made.
The other line of evidence that makes it “Zapotec” in identity is the Zapotec-style tomb (stone-lined cist typical of Oaxaca contrary to Teotihuacan’s simple pit interments) found with Zapotec glyphs on the of the entrance of the antechamber. In another part of the barrio, Paddock and Rattray found another disturbed burial in extended position, virtually absent in Teotihuacan but standard in the valley of Oaxaca. Associated with this burial was an urn of Monte Alban II-IIIA transition style (Nisa or Tani in the recent Monte Alban chronology) made from local central Mexico clays. Also, in the layer underneath the burial a second urn was found, this one probably made out of valley of Oaxaca clays. Also, near the principal temple at the TL7 structure, a ritually smashed Zapotec urn was found.
In terms of what this means there are two lines of thinking. The first interpretation, advance by Fowler and Paddock, is that Tlailotlacan was occupied briefly by a generation of Zapotec immigrants that, within a generation or two became fully acculturated to Teotihuacan practices. The other interpretation, advanced by Spencer, is that the ceramic vessels were items that served in the enculturation of younger generations by older ones, actively trying to maintain and display they Zapotec identities.
Spencer, Michael 1992. Tlailotlacan, A Zapotec Enclave in Teotihuacan. In Art, Ideology, and the City of Teotihuacan
Fowler and Paddock 1975. Nexos-Teotihuacan-Monte Alban vistos en la ceramica. In XIII Mesa Redonda de la Sociedad Mexicana de Antropologia, Arqueologia.
Paddock, John 1983. The Oaxaca Barrio at Teotihuacan. In, The Cloud People: Divergent Evolution of the Zapotec and Mixtec Civilizations.