No need to do both. I do one or the other depending on what time of yr and sometimes what I want to have going into the fall.
Let me explain a bit. Depends if the previous yr I had also done some WR blend and now is the rye headed out and going to volunteer seed from the old crop. If I want it to come back heavy in rye again I'll mow. That seems to me to put a lot of that volunteer seed on the ground and heavier germination. If I want to have heavier for clover I will cultipack the old rye which bends it over and covers the ground but not completely flat. A lot if not most of the old seed heads are not touching the ground that much and not going to reseed as heavy. Seems to come back mostly in clover which is my usual goal.