SEO, Backlink questions

hey all, I got a question
I make tumblr themes (link), and when people install my themes they have a install theme and credit button on the top right and bottom right (example), does it counts as a backlink and will it increase my seo score?
For example if "C blog" installs my theme, and she has the credit on the top right and bottom right, will my seo score increase? and I have another backlink right? and should I add "rel" to the "a tag" in the credit?

It surely does.

Yes, this is common practice. Website developers do this as a matter of standard practice.