The trigger/check is the game start. This means keeping the game running for weeks will not increase the Loyalty achievement. You can check your "first session time" in the options to know when a new day starts for you, but you still have to (re)start the game then.
I am sure that if you play through for a while you will realize that paying is optional. You can progress quite nicely. Visit the forums if you like and you will find a lot of info on where/how you get the most out the rewards on offer.
The trigger/check is the game start. This means keeping the game running for weeks will not increase the Loyalty achievement. You can check your "first session time" in the options to know when a new day starts for you, but you still have to (re)start the game then.