Amish, I went through several copies of 24-70 vc, before I got one which funcitons perfectly on my 5d3. by perfectly I mean, well centered, no VC issues, and accurate and consistent focus from all focus points. I had a well centered copy which had the exact problem yours does. Mine however focused accurately will the the vetical center points (up and down), but not if I moved laterally (to the sides).
I sent it in to Tamron, they sent it back, maybe slightly improved focusing, but much worse optically. Went back in a second time, without much improvement. went back in again, and I spoke to a rep which was very helpful and in constant communication with me. they tested the lens extensively, tried to fix it on my camera, could not, and then tested 3 different brand new stock lenses, before they found the one I have now.
The rep told me the AF of 5d3 is complex and problematic, whatever that means. I dont have an issue with my canon lenses.
So this one is great. Ironically, in the process, I was so frustrated that I bought the canon 24-70 2.8L II lens. I am having a hard time parting with tamron, b/c It took 8 lenses before I got this, b/c of VC, b/c its optically about equal to my canon. The canon is sharper at 70 2.8, if you look at 100% crops. Canon does better in the corners on the wide end, and tamron actually slightly better on the long end. The canon however, has blazing fast AF and also seems to do a bit better in low light with AF.
Hope this helps. So, you can return it and get the canon, send it in and roll the dice, but you have to be ready to spend a lot of time with repeat testing to make sure you have a good one, or just use it on your 6d.