Meaning
What does Don’t @ me mean?
The phrase “Don’t @ me” or “Don’t at me” is the brainchild of the modern man from the internet. It is a way of saying no offense on Twitter, where outraged people are prone to tag someone after an infamous post.
With this phrase, the tweeter may wash his or her hands and relax, because there definitely won’t be any consequence to whatever they said… just like giving out dating advice to friends but then adding “… or I don’t know.”
Origin
What's the origin of Don’t @ me?
The phrase was born in the late 2000’s; following the birth of the social media site, Twitter where people tag each other with the character “@”.
Since the spread of the site, the symbol became synonymous with calling out someone’s name.
Spread & Usage
How did Don’t @ me spread?
The phrase spread with the popularity of Twitter and the internet, where people got accustomed to getting tagged by the “@” symbol.
Now, with more people online, there are more dumb opinions, so the phrase is experiencing a height in popularity that will possibly only grow with the user base of the web.

External resources
- Urban Dictionary – Don’t @ Me (Don’t At Me)