Can we get back on topic please?
The idea of “15 minutes late with Starbucks” is derived mostly from the tumblr pastime of hipster-bashing. On tumblr, hipsters are mocked openly for their (usually) single-topic blogs that range from pictures of food to simple photography and amateur instagram pics. A common trend among these hipster blogs would be to take a picture of a Starbucks cup and post it online, so slowly and surely hipsters on tumblr became associated with Starbucks.
As an extension of this, white girl jokes became popular as well considering that the “stereotypical hipster blogger” is a white, teenaged girl. the white girls tag and the white girl tag are full of these kinds of jokes. (Click at own risk. NSFW content and pictures of white girls holding a cup of Starbucks are somewhat common in these tags as well)
Predating this, and somewhat similar to this 15 minutes late meme, is the slang term “Seattle Late”, which is a term that actually describes the event of someone arriving late because they stopped to get coffee.