I unloaded a bisque today, including several of these single-piece lidded jars, that are thrown as closed cylinders, then cut. One of them cracked in a pinwheel pattern. They always do when I forget one step, but let my error be your learning opportunity!
To prevent these sorts of cracks, after I cut the top off ("and after it's leatherhard...!" interjects Captain Obvious), I turn the lid upside down and trim out a small circle in the middle right where the dimple of the joining occurs. It may be the the trimming compresses the clay just enough, or perhaps it removes little microscopic cracks before they can turn into big ones; what I do know it that the failure rate without that step is pretty much 100%, and trimming stops pretty much all of it.