Your friend is right. In this sentence, 1993 is functioning as a noun. It is the name of a year, therefore it is a proper noun.
I worked at Starbucks could mean that you worked inside a Starbucks coffee shop. I could also mean that you stood in front of a Starbucks coffee shop begging for money.
I worked for Starbucks means that you were employed by Starbucks. It could mean that you sold coffee at the counter, swept the floor, or piloted their corporate jet.
Student or Learner