This is a tricky question. DevOps is a new concept and in any organization the maturity of DevOps varies from highly Operations oriented to highly DevOps oriented. In some projects teams are very mature and practice DevOps in it true form. In some projects, teams rely more on Operations team.
As a DevOps person I give first priority to the needs of an organization and project. At some times I may have to perform a lot of operations work. But with each iteration, I aim to bring DevOps changes incrementally to an organization.
Over time, organization/project starts seeing results of DevOps practices and embraces it fully.