Just to add to this - I remember asking this exact question during my VCI (PSI/PCI) class and have a penciled in remark about never getting a full year out of a vis (unless it's done on the first of the month). From the below - the answer is still not clear, but does have a recommendation. This is directly quoted from the Inspecting Cylinders book from the class (5th edition, page 83, authors William L. High and Mark A. Gresham):
"Many consumers and inspectors alike are confused about precisely when the next inspection is due. If my inspection was completed on February 15, 2009, what will the sticker say and when will the next inspection (if annual) be due? The month of February and 2009 (or 09 or 9), whichever way the year is represented on the sticker) will be punched out. Until recently, federal and industry policy established that the next "annual" inspection expired on the first day of February 2010.
The DOT retest due date was determined the same way. However, Hattie Mitchell, Chief, DOT Exceptions and Regulations Termination, has interpreted the hydrostatic requalification period to expire on the LAST day of the month. Nonetheless, PSI/PCI recommends that visual inspections continue to expire on the first day of the month so as to not exceed the established time periods."
So should an LDS argue a tank is out of vis because it expires the month (a year later) that it was certified - the argument is "recommends" and is not absolute - so as always your mileage may vary.
As I vis my own tanks - before I take them anywhere, I'll re-vis them if at that month boundary to avoid any/all arguments.