I was looking back at an ealier beta version of stackoverflow and noticed that tags were previously a fix in the site. When did they become user responsibility?
I think you are likely misinterpreting this:
Stack Overflow questions are grouped by tags, created by programmers just like you. Using the right tags makes it easier for other programmers to find and answer your question. Here's a list of all current tags, along with a count of how many questions each tag contains.
"created by programmers just like you" actually, sort of, means you can create them. Although, there may have been limitations in effect there limiting it only to certain reputation users, as it is now.
"Here's a list of all current tags" simply means that those are the tags currently created.
Essentially; that text does not suggest it was ever not the users' responsibility to create tags. In fact, it suggests it's always been.
Tags were always a user controlled function.
As you can see, the description on the tag box says :
"Combine multiple words into single-words, space to separate up to 5 tags (python c# ruby)"
Which suggests the ability to freely create a new tag.