When water leaks from one condo unit into another, is the owner with the leak responsible, or will the other unit's homeowner's insurance cover this?

A pipe burst under the kitchen sink of our condo. Water leaked under our flooring onto both the ceiling and floor of the unit below us. We did not have a personal homeowner's insurance policy when this occurred, only condo insurance. The owners of the condo below us do have homeowner's insurance, and we were under the impression that their insurance will pay them for their damages then seek payment from us. However, we have also read that their insurance should cover their damages and if we had insurance, our insurance should cover ours. As long as there was no real negligence involved, which I suppose is for an adjuster to decide, will we be held liable for their damage? Since we did not have homeowner's insurance at the time of the incident, are we ultimately responsible for bills the other unit's homeowner's insurance company may send us, or would we have to be proven negligent in some way in order to be legally bound to pay for their repairs?