With IaaS, what is responsible for handling the security and control over the volume storage...

Volume storage is allocated via a LUN to a system and then treated the same as any traditional storage. The operating system is responsible for formatting and securing volume storage as well as controlling all access to it. Applications, although they may use volume storage and have permissions to write to it, are not responsible for its formatting and security. Both a hypervisor and the management plane are outside of an individual system and are not responsible for managing the files and storage within that system.