Pipe burst in apartment above

Hi everyone! We are living in a rental apartment. As the title says, last night, the pipes burst in the apartment above us. We went up but the neighbour did not appear to be home. A plumber eventually managed to turn off their water supply from outside their unit.

Water leaked into our living room and kitchen via the ceiling, and bath area via the ventilator shaft and that removable cover thing in the ceiling. Even this morning there are rivulets of water still dripping down.

We are in contact with our rental management company, but we are also kind of worried about the situation upstairs. We are also worried about liability issues when our rental agreement ends. There is definitely going to be damage to the wallpaper, and maybe mold problems as a result of this incident. tWho else should we notify? Mainly we have not had very good experiences with this real estate company so far so we want to be fully prepared for next steps which they may not tell us. Thank you!

by tropical_sushi