Hi Holgar,
The Gregorian Calendar was aligned to midnight, it is doubtfull that midnight could be measured accurately by water clocks, the minute hand to clocks was invented five years before the Gregorian Calendar, pasted below:-

" Minute Hand

In 1577, Jost Burgi invented the minute hand. Burgi's invention was part of a clock made for Tycho Brahe, an astronomer who needed an accurate clock for stargazing. "

[www.thoughtco.com]