Omni-Channel can be one of the most powerful tools in a Salesforce admin’s toolbox. It is a configurable tool that allows you to intelligently route leads, cases, or other work to the most appropriate individuals. As an administrator, you can determine how you want to assign the work and what attributes are used, capacity in units of work for each users, and even the skills and experience level per skill that each user possesses.

TL;DR - Omni-Channel doesn't trigger any automation. Build your automation on the Agent Work object...