Read the lease. The insurance and indemnification clauses will define the limits of coverage. Then get a copy of the declarations page of the condo assn. policy. Have both reviewed by a trusted insurance broker familiar with commercial property (i.e. not residential), especially the clauses regarding co-insurance, which is not what it sounds like. Co-insurance is actually additional deductible from total coverage.
As a matter os practice, the tenant’s policy and the condo policy will pay in order of respective liability limits. In addition the lease may have language that protects you from any claim over and above the policy limits, i.e. indemnification. This is almost always the case with credit-rated tenants who self-insure.
That said, to protect against lawyers like John Merchant noted who sue everyone in sight, we carry an umbrella liability policy with coverage across all properties, including the triple-nets.