If you made the chairs, you have discovered why you wish you had made the back rail an integral number of seating material widths wide. In your case, 13x1" or 14x1".
There are three possibilities to deal with this 1/2" problem: sew a loop over the back rail, space out the 1/2" gap among the 13 winds of the warp, or make 14 winds of the warp.
I like the loop best. Before you start winding on the warp you take a short piece of tape and sew it in a loop over the far side of the back rail. Use a piece of string over the front rail to pull this loop fairly tight (and make sure you cover the string as you wind on the warp). So the last wind of the warp will partially cover this loop as it goes over and under the back rail, around the inside of the back leg, and out the side so you can start the weft weaving. This will leave just a little of the loop visible but cover the entire back rail.
I think this is a better way to go, rather than spreading the 1/2" gap evenly across the 13 winds of the warp, which is another alternative. You want to keep your weaving as tight as possible. The third alternative, making 14 winds of the warp, will cause new problems as you start to weave the weft so I would discard this idea right away.
As you weave the weft it will tend to spread the warp out a little anyway. If you have not done this before, it is important, as you weave the weft, to keep pushing it back to keep it parallel with the front and back rails. Otherwise you will have a very hard time with the last two or three rows at the front of the chair.
You could experiment with these ideas by winding on the warp and then weaving a row or two to see how it looks. The nice thing about weaving a seat with shaker tape is that you can take it apart and start again if you don't like things, even a year later.
P.S. The loop idea can also be used to deal with the inevitable spaces on each side of the front rail. The traditional way to deal with this is to back weave tape after you finish,which leaves loose tape in the seat. Instead, sew loop(s) on each side of the front rail before starting the warp. Tie them off with string over the back rail. These loops need to be a little longer, and you will incorporate them into the pattern as you weave the weft.