The fact that there is some wood left on some elements of the tube indicate that the tube is noy revolving around the headstock/tailstock axis evenly, and as Steve has said, your mandrel could be bent, or you could have tightened the knurled nut up too tight. If the mandrel shaft is bent, and you can tell by taking it out and rolling it on a flat surface such as a kitchen worktop, you need a new one, trying to straighten it doesnt work. If it is straight I would suggest that you have overtightened the nut, but check the tailstock is aligned with a kiss test, the tailstock could be off centre.
The reason that you are splitting the wood could be, as Steve says, that the parting tool is blunt, and if you have been attacking the tube it will at least have lost its edge, but if the wood is reasonably soft you may be attacking it horizontally and scraping away which will have the effect that you describe.
Sharpen the parting tool,
Attack from the right angle and
Sort out the misalignment/off centre rotation and the issue will go away!
