TAB is an initialization, not a term in itself. When I get home later today, I'll look through my books to see if I can figure out what they're referring to. Here's some crochet terminology-- To "join in a ring": chain the required number of stitches, then put your hook thru the FIRST chain and pull up a loop, this will make your ring. A "long end" is a few inches longer than you need to complete the required action. I always err on the side of caution. "Fasten off" means that you finish your last required stitch, then cut off the yarn in a long tail (long end) and pull the thread thru the last stitch and tighten it up, then you weave in the end.
YOUR PATTERN: (ch 12, fasten off, join in ring at top of tea cozy) I assume that this is to be a ring to lift the tea cozy off? Since I haven't seen your pattern, I can't tell you what exactly to do, but now that you have the terminology, play with it a bit and take a close look at the picture and I bet you can figure it out. I can only guess that you chain 12, fasten off, then put the hook thru the designated place at the top of the cozy and then the first chain stitch, and then pull a loop of the tail thread thru these holes and fasten off again.
I find that crochet edging books don't really bother to explain how you're supposed to start crocheting onto another object, especially pillow cases. It's very frustrating, I agree.