I'm brewing a Belgian Pale Ale on Monday (12). It's my first time and using BeerSmith has been of great help. These last few days have filled me with a whole lot of doubts though. After fermantation is done (2-3 days with the same FG value) I'm gonna drop temperature down to 10 °C for maturation. On Beersmith it says under Carbonation and Storage tab that keg/bottling temperature is 21,1 °C, carbonation used is about 175 g DME, aging time is 30 days and storage temperature is 18,3 °C. Is 30 days the time I should leave the beer in the fermentation bucket maturing at 10 °C or the time i should leave the bottled beer resting? If the latter, how long should I leave beer for during maturation?
Don't rely on Beersmith/software for the timing of any stage of the process. Brewing is predictable to some extent, but it's not that clear cut.
Ferment your beer until it's done. You already see to understand the stable FG rule so that's good.
After fermentation, you'll transfer to a bottling bucket and add your sugar. You want the beer to condition (carbonate) at room temperature in the bottles for a couple of weeks. For the carbonation process, it's always better to wait a week at least, then simply chill one bottle and crack it open and see if it's ready.
As for aging time for flavor improvements or maturation: software absolutely can't help you with that. There is no formula. Once the beer is carbonated you can chill it down to fridge temps or keep it at cellar temps. Most homebrewers just drink the beer as they want. It if seems to peak in flavor or seem to start to decline drastically, we usually invite friends over and drink it up.