I wrote previously about getting seams to line up properly. Here is goes again.
If, when you are sewing along, your needle comes first to the cross seam, the act of sewing will tend to push the seams apart. If you position your fabric so that the needle comes to the (top) seam allowance before the cross seam, the seams will be locked in the right place as you sew.
Yes, you should press the subunits first. Yes, you still need to slide one unit against the other until the seams butt against each other. Yes, you still need to pin.
I have been one of many quilters working on a project together. This direction of approach makes all the difference between speedy completiion and frog stitching. Some projects don't lend themselves to doing this waydue to previous seam allowance directions. I often do it anyway, then clip the seam allowance to let it lie back where it should be.
Here I am making a pinwheel.