Pressing a whole quilt top, or a back built up from pieces, tends to be treated as one undifferentiated chore, something to get through before the interesting part begins. Yet it has an order of its own, and following that order saves time at the board and heads off faults before they are ever quilted in.
The sequence is where the real saving lies. On your first pass, press only the seams that fall to the left, skipping the rows that fall the other way and leaving the horizontal seams entirely alone for now. Work steadily down the top, touching only those left leaning rows. Once they are done, turn the whole top a hundred and eighty degrees. The rows you skipped a moment ago are now the ones that fall to the left, and you repeat exactly the same pass over again. The reason is worth understanding, because it is not fussiness for its own sake. A right handed presser works most surely when pulling the iron towards the side she has the most control over. Turning the top so every row meets that same confident motion, rather than switching the gesture round for every other row, keeps the pressure even and the seams truer from one end of the quilt to the other.
Where you sit the work matters just as much as how you move the iron. Line the edge of the top up with the edge of the ironing board, so the iron can travel right off the end and reach into the intersections without leaving little pockets it never quite gets to. Shift the top along as you go, keeping the row you are working on square with that edge.
The horizontal seams come next, and they are where puckers like to hide. Before you turn a seam, give the closed seam a light touch of heat first. That relaxes the stitches, so the seam settles in the direction you want with far less resistance when you open it out. As you open it, walk the seam along with your fingertips just ahead of the iron, rather than letting the iron shove it along on its own. That point, right at the intersections where several seams meet, is exactly where the small pleats form, the ones you never spot until the top is already under the quilting needle and much harder to answer.
Not every fabric behaves the same way under heat. Blends carrying polyester and brushed cottons tend to resist, springing back and shrugging off a single pass. These often want a second pass, or a clapper pressed down firmly over the seam to draw the heat out and lock the fold in place as it cools. A moment of patience here settles what a hot iron alone will not.
Press in this order and the top reaches the quilting stage flat, square and settled, with the seams already lying where you meant them to and nothing left waiting to pucker under the needle.