There are several reasons for puckering. 1st is the density of many designs- some just have too many stitches. It may help if you can enlarge the design a little on the machine, without increasing the number of stitches. 2nd is that with the straight-sided hoops, just a small amount of slippage of the fabric allows more to pucker. This doesn't happen with round hoops used in hand embroidery. Sometimes I pin fabric to the backing- not where the needle or foot has to go- at the top bottom and sides, especially with the large hoops. I also use starch on my fabrics, not the bought spray on kind, I mix my own and spray on. Doesn't have to be as stiff as cardboard though. I do this with patchwork as well as I find it easier to cut and sew the fabric. Lastly, these days I mostly use a wash-away adhesive backing, and sometimes A4 copy paper- tho thats a no-no to some, it eventually washes away too. You can also try using a slightly looser thread tension.
Hope this helps
Cheers....