If it's machine applique, the most common cause of puckering is not stabilizing the background fabric.
Most people use some form of stabilizer underneath. I prefer to heavily starch background fabric with a 1:1 solution of Sta-Flo liquid laundry starch and water. I "paint" this onto the fabric with a large wall painting brush, toss the yardage in the dryer, then iron with steam. The fabric becomes fairly stiff and very stable. I cut out the background square larger than finished size in case there is any distortion from the applique, then trim to correct size afterwards.
Basically what happens when the background is not stabilized is that the background fabric tends to get stretched on the bias so that, by the time you get around to where you started, there is a little more background fabric than applique. That creates a pucker.
I should add that I do machine freezer paper applique, not fusible applique. I'm not sure if fusible will stick to starched background fabric; would have to test it first to make sure.