Tây ơi! Tây ơi!

I went to the market this morning to get the few grocery items that I always get every week: vegetables, tofu, chicken, mint, and fruits. Usually, I speak just enough Vietnamese to get by and come home, but Grace always wants me to socialize with these ladies because she thinks it's fun. As I walked through the fruits aisle looking for some good fruits to buy, I had my hat down low so that these ladies wouldn't know that I was checking out their produce. I tried to avoid making eye contacts or letting them know that I might be interested in what they had to sell or else they would be calling out to me and begging me to help them out by buying something from them.
All of a sudden, one lady started yelling out, "Tây ơi! Tây ơi!" (westerner! westerner!). I looked back and smiled, shaking my head signaling to her that I was not interested. But then I remembered that I was supposed to socialize, so I yelled back, "Không phải Tây, tôi người Việt!" (I am not a westerner, I am Vietnamese). Pretty soon, a few ladies congregated around me, checking me out and asking me questions to verify that I was indeed Vietnamese. After a while, one lady conceded that I was not a westerner but must be racially mixed. Then I told them that my parents are 100% Vietnamese. They looked at me from top to bottom, and then one lady said that a Vietnamese wouldn't have a nose like mine. Another one followed with, "And you have hair on your arms!" By the time I left, they were still not convinced. I walked away with 4 nice looking mangoes that I bought from one lady and 3 pears from the lady next to her. They were still calling me Tây as I walked away. Tây or Ta...?