Uhh ... might I assume that you are using the carbide squaring jig? These have only 2 cutting heads, and damaging blanks is a known issue ...
The other major problem is that those blanks were FROZEN.
If you're gonna be working in those temperatures, keep the materials' weaknesses in mind ... CA (superglue) doesn't like temperature extremes ... hot (think too hot to hold) is bad ... melts the acrylic (cyano-acrylate, creates an acrylic when cured), and cold (below freezing) is bad ... makes it brittle, prone to cracking or shattering.
Certain types of wood, especially oily woods, don't dry out very well or evenly. Freezing affects these types of woods badly ... olivewood can contain traces of olive oil. Colorgrain is a layered pattern of plywood held together by superglue... Cold affects both of these very badly.
Another major issue is the squaring jig itself. You'll have MUCH MORE success by taking the bit (the 1/4" rod) in that jig out and putting it in BACKWARDS ... and then punching a hole in a small piece of 220 grit sandpaper (or lower, 120 might work OK), and gluing it to the flat side of that squaring jig ... use it as normal in that position.
Don't forget to ream the brass tube after ... and don't forget to WARM UP YOUR SHOP before attempting to turn those on your lathe ... oh, and warm the blanks up too. In fact, you may want to either maintain heat in the garage/shop or move the essential items you need into the house to keep them warm.