Datacenter soc certified

I'm taking over a IT department at a SaaS firm, they have all their servers at a Colo that is soc certified. The management team at the firm believes long as the datacenter is soc certified so is the company (SaaS) firm. All of the servers are owned by the SSAS company, the datacenter is only providing space power internet. Is this correct?

Or the SaaS firm needs to undergo its own soc qualification and audit process.

Also if the …

certified cybersecurity datacenter soc