These are based on opinions and may not be true. These should be viewed as advice unless proven undoubtedly true. Check comments for confirmation. Results may vary.
In any given mission, there is a low chance of a single Rare Storage Container spawning somewhere in the map. If one spawns, it will randomly select a vacant high-value hotspot, similar to that of a Syndicate Medallion, and spawn in it.
Trials have significantly increased chances of encountering Rare and Reinforced Containers, to the point that as many as six may be found over the course of a single Trial. The modified tileset of Trials includes several designated spawn points for these containers, which can speed up your search if you know where to look, though they have occasionally been known to spawn out of bounds or in walls, making them inaccessible.They can be blown up with explosive weapons however and the rewards can be collected via carrier
Dark Sectors seem to have an increased chance to spawn Rare and Reinforced Containers. While it is not nearly as high as Trials, it may be somewhere around the map. If the mission is defense, it is worth spending a little time to check the map for one because typically there are no regular containers.