Animations will stop working when you close the game, but you don’t have to worry about your offline earnings because you will be earning the proper amount according to your current in-game progress.
However, the game needs to restart animations from a specific spot and some prison services could be affected by a temporary loss of productivity: for example, if you enter the game during lunchtime, this meal could be lost and prisoners should wait until the next one. This could happen with other services, but the game is fully tested and these temporary inconveniences are known and expected, and they will be solved in a few minutes of gameplay. 
Please remember that your offline progress won’t be affected by this visual restart. 
The team is still refining this feature to give you the best possible gaming experience.