That is the way the cookie crumbles with metric rounding.
A 225 is only a 225 when mounted on a 70% rim and inflated IIRC to 35psi ..... and it's a sidewall section spec, and is rounded to the nearest 5mm on the 5s. So 70% of 225 dictates a measuring rim of 157.5mm or 6.2 inches. which rounds to a 6" rim. The tread width is supposed to be, in your case 60% of that 225 or 5.3 inches
But here's the deal, that 225 could be as little as 220 or as much as 230 and still be rounded to 225. and that makes the tires tread vary by 60% of those 10mm or from 5.19 to 5.43, strictly by the math. This however only indicates a treadwidth variance of .24
If you install a 225 on a different width rim than the 70 percenter, then the section width changes. And if you then math the tread from the new section width then the profile maths out differently as well.
And molds are a whole different animal. Some manufacturers roll the sidewalls up early and others add some rubber on the edges. This could easily account for another .26 to equal your estimated 1/2" difference.
Of course anything over 3/8 inch can be rounded to "about 1/2 inch", soooo then there's that too,lol.
But I do understand your perturbation,lol, unh,perturbement?, unh, well you know. Not dismay, not concern, not confusion,not ......brainfart; can't think of the word.......