Mining income is earned every season, regardless of the good or bad harvests, regardless of whether the city is under siege...

I noticed a similar correspondence between the number of mining hills shown on the map and the return mines give you. There are two types of mining places: the smaller copper ones and the bigger gold ones. The former gives you a 600 per mine, the latter gives you more.

However, some provinces (like Arretium) give a mining symbol, but no possibility to build a mine, which makes me belief the markers on the map are there partly for animation purposes. Therefore I too advice to preview the mining income in the settlement details by listing the mining complex in the recruitment viewer.