Your lease controls. Someone should review it. Termites swarm and can occur rather quickly. Damage however usually occurs over some time. You should determine the status of the furniture and the treatment needs or replacements requirements before you start requesting the landlord to be responsible. They probably will be responsible for the lodging for one or two nights while the tenting occurs, unless they do a spot treatment that does not require you to move.
Your lease controls. Someone should review it. Termites swarm and can occur rather quickly. Damage however usually occurs over some time. You should determine the status of the furniture and the treatment needs or replacements requirements before you start requesting the landlord to be responsible. They probably will be responsible for the lodging for one or two nights while the tenting occurs, unless they do a spot treatment that does not require you to move.