When the game creates a mission for you, the first step is to select the station from which the mission is generated. This can be any of your stations but there is a mechanism to make sure that coverage areas that currently have no open missions will get regarded.
The game then filters the mission list for the mission type corresponding to the selected building and for missions for which you fulfil the requirements. It checks of you have the needed buildings and extensions. If the selected station belongs to a coverage area it only takes buildings into account that belong to this coverage area. It also checks if an ambulance station is available and will otherwise not regard missions that generate patients.
From this filtered list of missions the game will then select the mission it generates. Sometimes certain event missions have a higher probability, but otherwise it is a random selection process. If the mission doesn’t have a POI it will randomly select the point where the mission takes place. This can be any address within 2 kilometres (1.2 miles) from the station (for some special missions this radius can differ).
If the mission requires a POI the game checks if you have set this POI within the 2 kilometre range. If you didn’t set the required POI in this area it will check if at least 2 players have set this POI in the same position. If the game can’t find a POI in the area it will not generate that mission and the mission generation process starts once again.