Tenant civil liability and private civil liability are two different things.
Tenant civil liability covers you in the event of accidental damage in your accommodation. It also covers you if this damage affects your neighbours, for example if your washing machine floods your apartment and causes a leak in your downstairs neighbour’s home. In that case, tenant civil liability takes care of it.
Private civil liability, on the other hand, covers bodily injury or material damage that you may accidentally cause to others. For example, if you accidentally break someone’s phone, private civil liability will step in to cover the damage caused.
In short: tenant liability = your apartment and the neighbourhood, private liability = other people in everyday life.