In any case, most water mills were built on cuts along river meanders, and do not occupy the same space in the landscape as irrigation. In that regard I don't see a whole lot of sense to make them mutually exclusive per sé, but setting up boundary conditions for both seems logical.
"China’s feudal society not only stipulated the order in which water resources are used, but also imposed some
restrictions on the scale and time of the application of water mills. According to the “Shuibushi” of the Tang
Dynasty, “Water mills could be used from August the 30th to January the first in next year. For the rest of the
time, the government sealed water mills under the sluice gate. But when the seals were relieved, they were first
to use for the irrigation.” It could be seen that water mills were allowed for use in only four months each year in
Tang Dynasty. During the Ming and Qing Dynasties, according to the “Tongli Canal Book” excerpted from
“Water Conservation in Hongli County”: “Water mills in the villages had been abandoned for a long time due to
the impermanence of the canal water. And it won’t be restored. Offenders would be investigated.” It could be
seen that during the Ming and Qing Dynasties, it was forbidden to rebuild machines that run by water. In
addition, the “Tongli Canal Book” also limited the time of the use of water mills. “The use of the water mills in
each canal were personal interests. Water conservancy was related to the lives of people. It was planned to stop
the water mills from the beginning of March to the end of September every year. And during November to
February, it was leisure time for farming. As were shown in advance every year. Violators would be punished
severely.” "
Source (Edit: fixed source link)
So at least in China there was a clear conflict between irrigation and watermills.