I believe in this case that the reference to "noon, on the 16th instant" is referring to the 16th day of the month, not the minute after 12:00 - so, he died at noon on June 16. Encyclopaedia Britannica lists his date of death as 16/06/1858 (https://www.britannica.com/biography/John-Snow-British-physi...)
Being minute-level precise about quantities that can't be known to the minute isn't exactly something to point to to suggest that their other coverage was uncharacteristically sloppy.
"Instant" means the current month, "ultimo" refers to the previous month and "proximo" the next (https://www.oxfordreference.com/display/10.1093/oi/authority...).