Yes work with square material if doing specific designs. If using oops pieces make sure they are the same dimension all around. You can stack your pieces on the tube and build the segment like that or you can build the blank and drill all at once. If you stack build then you drill each piece individually and this is the easiest way to avoid blowouts. But some designs can not be done that way and thus you need to always work from a square stock. Every piece or design you add needs to be square to the main body. After all this is done you need to find the center of the design and drill it. Many times this is not exactly the center of the blank. But if you build the design on a square blank many times you can just find center of the blank and drill. I hope this is clear. I will show an example of a stacked segmented pen first and then one that is not. But to answer your question square is the key. and keep that way throughout the build. The last thing if drilling on the lathe you need to chuck the blank square. Again the type chuck you use needs to allow for descrepency of off center drilling. I prefer a pen chuck, one similar to PSI but I use a Vicmark version.
That is the specific type in which drilling and stacking has its advantage. However, one must make sure everything is square. Making it square is done with larger pieces and then slicing them with a precision saw. ON occasion there are posts here concerning a precision mini table saw. They are not absolutely necessary but they do help in many cases. I made my own years ago and below are an overview / two photos. Therefore my "slices" are dead on accurate and square. I drill holes in squared blanks, measure how thick I want each section and then slice.
That is how I center and round my blanks too. Find center of pattern and round it true. So easy from there.
