If you are playing an Adventurer's League game, then you use the Adventurer's League rules as laid out in the FAQ.
If you are not playing an Adventurer's League game, then you use the normal rules (unless your DM says otherwise).
The Adventurer's League has a different set of rules for the management of Downtime. In a normal D&D game, downtime is actual time spent, in-story, by the characters not adventuring. If your party just finished a major quest...you all have to agree to take some 'time off' as downtime, rather than just continuing the adventure.
In an AL game, where 'timelines' are a completely wonky mess as you hop between DMs and campaigns and discrete, unconnected modules...downtime is a currency that you earn at the end of any adventure, and can spend to do 'downtime activities' to improve your character in incremental ways
Downtime. At the end of each adventure, your character will earn downtime, which you can spend on downtime activities.
There are many things that downtime is expended for.
- A Wizard scribing spells into their spellbook
- Any Downtime activities prescribed in the PHB
- Additional cost required to pay for spellcasting services
- Advance to the next tier of play (4th, 10th, and 16th level you can spend an increasing number of downtime days to level up.)
- Trading magic items with another AL Player
And so on.
In short, because Adventurer's League has you carrying the same character around between countless different DMs and Adventures that don't have a consistent timeline shared between them, AL introduced 'Downtime' as a payable currency that is earned and spent.
Ideally, you'd have "120 days of actual in-game time" pass before your Clone was ready. But trying to track that time in AL is an exercise in abject futility, because there is no consistent, reliable timeline...hence: "120 total days of Downtime expended."