I'm glad I took too Aleve because all this makes my head hurt. To begin with there does not appear to be complete information. However, in rereading your original post which says you cut a square of 4 7/8 inches and then cut the square into a triangle. My quiltmaking knowledge tells me that the intention is to sew two of the triangls together back into a square. With the 7/8" the assumption is that you are going to sew them together with an accurate 1/4" or scant 1/4" seam which will make your square 4.5"
However your illustration does not show a half square triangle square. So something is missing. So I don't understand your original question related to what size you should square up the square, according to your description it should be 4.5". Your illustration does not match your description. To my knowledge no instructions assume trimming down unless they tell you to. 7/8" is the basic addition to sewing triangles into square. I've talked enough.