Trouble is intended to allow you to trigger things that only otherwise happen at a longer time scale than the one you’re working at. In the current update, that doesn’t explicitly include year long operations and moves, but there’s no exception made for them either (there is one for 3D printing).
The operation and move resolves when you make the trouble roll that results in the year long action. You make the decision what you’re going to do and where you’re moving and the total sequence resolves instantaneously. For operations it is assumed you started a year ago. For movement — well. What is completely abstracted away in the High Frontier rules is the fact you actually decided where you were going at the point you launched the rocket; and map movement is just a convenience that allows you to plot out this movement over the time it actually takes rather than pre calculate the entire path. It’s really not clear that’s how the game works until you start to look under the hood.
As for how often you should roll; you should do it for any action which consumes resources that are not easy to replace (top of page 23 in the Crewed Rules). This includes any actions that happen at a time scale where you’re using up oxygen or power without a good way of replacing these (eg you’re not carrying enough solar panels to last a full day/night cycle).
For base construction, this should be any action that is long enough to trigger an event that puts your population at risk. This is normally annually but might be every week if the base is starving.
However you’re correct in noting that if you’re working at a small enough a time scale, you never have to roll, which means you never trigger trouble and therefore never use up resources. I don’t have a solution I’m happy with here yet — I need to force a minimum number of rolls per turn at these smaller scales but I don’t have a clean way of doing so.