Condominiums almost always carry a master insurance. It typically covers only the common elements. This is typically sufficient to a lender. However, what is within your unit and damage caused by your unit to others is typically your responsibility (like damage to hardwood floors, appliances, custom paint and draperies.)
Most leases by realtors use the NVAR lease which requires tenants to have renters insurance. That will typically cover the tenants belongings. You will want additional insurance to cover your liability and damage from your unit to other units. In condos, this would typically be water leaks from your unit to the units adjacent and below. Leaky showers, washing machines and water heaters are just some of the things that can go wrong and the damages would be the owners responsibilty if they do not have adequate insurance.
In your case, the condo association will probably cover restoring the common elements part of your unit. The owner causing the leak above you would be responsible for the damages to the inside of your unit and the belongings of your tenant. Any rental loss and hotel expenses may or may not be covered as well. Some condo associations are helpful in dealing with the insurance companies involved, others will have you run around yourself. Personally, I would speak to the owner of the unit that caused the damage and find out if they have insurance and go from there.
Hope that helps - good luck!