Have a step in your build process that’s scoped to your dev/test environments that deploys your web app to azure. Since this step will be scoped only to dev/test, it’ll only run when you deploy to those environments.
If you are doing your first steps with Octopus, I personally recommend you to start with the Octopus part of the above process, until you understand how to set this up from the Web UI. Once you have deployments flowing to Azure and IIS as expected, then start dipping your toes into the integration with VSTS.