I don't know what mill you have. I looks from the picture that it's an R8 holder.
So, first, determine in your spindle is running true. Check the taper in your spindle with a test indicator. If it is off, the face mill might not be the problem.
If the spindle looks good, check new inserts in the cutter (the bottoms, radius tips and sides) with your test indicator and get some readings. Check them as you revolve the spindle by hand very slowly over the cutting edges. Mark each flute so you don't get your recording mixed up. Depending on what you find, maybe you can tweak the pocket with a small, fine, file. Be careful, because you could do more harm than good, but if it's only off a thousandth's or so, a slight touch, or burr removal, might be all it takes.
So, first, determine where the problem is. Then, address the problem
Good luck,
Ted