I’m not sure what you mean by tied roll? The number on on the die is how many obstacles your swarm needs to beat to capture the room. The swarm roll is basically an engagement roll that you roll once at the start of a room to determine your narrative position. Afterwards, your individual rats make a roll in the same way other ttrpgs ask characters to make rolls. Basically when a rat is performing something in the fiction, you make a roll to see how they do. Thats when you refer to the table in the making a roll section to see how they did. The only time you introduce a threat is during the swarm roll, which is when you enter a room for the first time.
If you read the section on swarm rolls, you’ll find it says: “ If any die is lower than your swarm’s notoriety, introduce a threat and reset your notoriety to 0”.
The threats persist, that is why it is favourable to try to reduce and remove a threat!
Hope that helps.