A multiplicity of things can cause this. All but two are related to the mandrel characteristics. TBC, turning between centers will eliminate most.
Here is a thread that is not directly related but OOR is mentioned a few times as well as TBC.
I am on a fact finding mission. Can you help? What do you wish you had known earlier in pen turning? or in different words: Knowing what you know now - IF you could go back and start over in pen turning - what would you skip, change or do differently? answers for instance: - I wish...
www.penturners.org
OOR (out of round - not "technically" correct but for laymen's terms, it works well). Is caused by:
1. a bent mandrel (even a minuscule bit)
2. tail stock pulled up too tight, forcing a minuscule bend in the mandrel as it turns
3. poor fitting bushings ( rather loose)
4. ends of the blank(s) not perfectly square or tube ends not square
5. slightly dull tools that require a bit more pressure to turn the blank down. Sharp tools are needed!!!!!! Let the tool do the cutting, not force/added pressure. This force - puts pressure on the mandrel causing OOR.
6. heavy sanding, particularly on softer woods. The softer wood between the hard ridges sand off quickly causing OOR.
7. Wrong Live Center in the Tail Stock. The mandrel has a dimple in the end that fits up to the Live Center of the Tail Stock. MANY talk stock live centers are much more pointed than the one that is actually needed. You MUST HAVE a 60° Live Center to fit into the dimple of the mandrel. IF NOT, the very pointed one - the very tip of the pointed one will ball up or bend (might need a magnifying glass to see it) and will cause OOR. Quite common for new pen turners.
8. Loose tail stock, not tight enough.
9. You have already checked tail stock and head stock alignment.
TBC will or can eliminate problems 1, 2, 3, 5, & 7, and in some cases 4. It Looks like you ARE using TBC, then the problem is loose bushings in the tube, or not square blanks combined with a lot of pressure, forcing it OOR/no concentric.
Second Thought, In Some cases, while the lathe will line up tail stock to head stock OK - they "can" be locked down out of alignment in some cases. Might be yours