try lengthening your stitch-
one thing about applique is...
it NATURALLY draws up the fabric a little bit-this is why we cut our squares an inch larger than needed, do the appliques then trim the blocks...the process of applique and embroidery cause the fabric to draw up a bit...it is normal- the process of the technique you are using- the drawing up sometimes looks a bit like puckering---you should be able to press pretty flat--but the fabric will still be drawn up a bit- you are not doing anything wrong. If it is actually PUCKERED a looser stitch may help...but if it is simply the natural drawing up- ...
even when hand appliquing it still draws up.
for machine applique i use either an invisible stitch, zig-zag or blanket stitch- with a stablizer- unless i'm using fusable (like heat n bond lite) which is a stablizer on it's own.