Each player has a Time Bank for every Online tournament they play in. This is an extra amount of time outside of the 15-18 seconds every player gets to take an action when it's their turn.
Usually, this is set to 30 seconds per player at the start of the tournament. Any time a player activates their Time Bank, they have that allotment of time left to act.
As the tournament plays on, every 30 minutes or so, 5 to 10 seconds are added back to every player's Time Bank automatically.
If a player is disconnected from the game (via bad connection, internet outage, etc.), the system automatically gives them an additional 60 seconds to re-connect. Once the system detects their connection, they will have a short time to act. This is the same for all players.