Help with sleeves (DMK Reversible Tunic Top)

I am new at doing sleeves and am trying to make the DMK Reversible Tunic top.  I have made the outer shirt and am trying to put the sleeves in.  It tells me to put them in, then pin and baste, then sew in from top to bottom one side then the other. The problem is... the sleeve does not fit in properly.  It is too big around so it will end up maybe kind of gathered looking or something... but sewing from top down that gathering would end up in the armpit.  Does that make sense?

I thought I sewed my seams quite well.  I checked both sleeves and they are both the same so it seems that my sewing was even and so hopefully right?

Any advice here?  This must have happened to someone else before! I am not sure what to do at this point.  Go against the directions and try to make it so the fabric has a gathered look at the shoulder, or

Any help would be appreciated!

Thanks so much!

Have you double-checked your seam allowance? I would make sure everything was sewn with the correct seam allowance because a little bit off, can result in the sleeve not fitting well.
Have you already tried pinning it into place? Sometimes as you sew, things will get stretched out so that what seems to not fit at first, will fit perfectly once everything is sewn in place. This might be why the pattern calls for you to baste first, then sew a regular stitch.