Hello & welcome to the board!
Many quilters will relate to your jumping in with both feet!
As I understand it, you have cushion inserts that are 16X16", and have cut 4.5" patches. You are planning on arranging them in 4 rows of 4. You have actually cut them correctly. In quilting, we use a 1/4" seam allowance. A cut 4.5" patch, if perfectly sewn, will come out to a perfect 4" square. From what you are saying it sounds like your seam is a bit too wide so your patches are a bit too small. You have 2 options: either un sew them & re sew with a narrower seam or complete the pieced section and add strips of fabric around the perimeter, creating a border (the log cabin suggestion).
Here's a tutorial on determining the correct seam allowance:
Achieving an Accurate 1/4" Seam Allowance
One other thing to check is pressing. You should be pressing as you go. Sometimes you can get a tiny pleat in the seam which will throw off your measurement.