Welcome to the board!
First off, two 6.25" x 12.25" strips will not result in a 12 inch finished block. Allowing for half inch seams, the strips need to be 12.5" (a quarter inch at EACH end) by 6.5" (again a quarter inch at each edge).
There are 3 main areas that can affect your accuracy: cutting, sewing and pressing. First cutting. Sounds like you are approaching your project carefully, but here are a couple tips,
Cutting: don't use the lines on your cutting mat for measurement, only to align the fabric. Use a single brand of rulers for your whole project. After you cut a couple pieces, measure them to make sure your rotary cutter isn't wavering.
Sewing: You really don't measure the seam, you measure the resultant patch. Here's how to check:
http://www.quiltingboard.com/tutoria...ce-t89997.html
When you start sewing long rows together, you have to pin the intersections.
Pressing: make sure that you are not pressing a tiny crease into the seam, or that you are using so much pressure that you are distorting your fabric. If you are using steam, try a dry iron or vice versa.
And finally , it's best to square up the project as you go. This means that you sew two 6.5 X 12.5 inch blocks together, press, then use a ruler to make sure you have a block that measures 12.5 X 12.5. You don't want to wait until you sew the whole thing together to discover the issue.
First quilts are always an adventure! Cut yourself some slack. I personally would just quilt it as it is and call it a learning adventure. If you really want to fix it, and you really cut your strips at 12.25 X 6.25, the block will measure 12.25 X 12 if sewn perfectly. Take the top apart, measure all the blocks to see what is the smallest. Then just cut everything down to that smallest size square so you start with the same size blocks.