A couple things that might need further explanation:
Neck tension is set by your expander ball as you cycle the case out of the sizing die, therefor you need to measure the expander ball. Should be right around .222" as the bullets should be .224". Check both of these things and see how they measure up.
Crimping may or may not be necessary bullet depending if you have good neck tension. I use a Lee FCD for every load. For bullets with canellure I lightly crimp into the cannelure. For bullets without cannelure, I just use the FCD to remove the very slight expansion from the M-Die I use when I run on the progressive, so just a kiss. I dont like using a taper crimp as the potential for something to go wrong is much higher and it isnt as sensitive to trim length on case.
223 and 5.56 brass are exactly the same thing after being sized with a 223 sizing die and trimmed to length. There are very minor differences in the case if it is factory ammo which is why they say dont shoot 5.56 in a 223 barrel.
You do need to FL size all semi auto rifle brass. Neck sizing is for bolt guns, and those even need FL sizing every 3-4 firings.
As others have said, test your neck tension with a dummy round. A crimp is not an alternative to proper neck tension.
You may also be experiencing some spring back. When 223 cases get around 4-6 loadings, the necks get work hardened and will spring back. Your expander might be .222, but post sizing the case opens to say .223 which is will reduce neck tension a great deal. Actual count that is takes depends largely on brass brand. LC brass is generally very good, and should see 5 or more reloads before it gets really work hardened in my experience.