My app uses the Salesforce API and a managed package. Inside of the package, I have a connected app using OAuth and the Rest API. When the package has been installed, are users redirected to the call back URL? I need the package to be installed and users to pair our app with Salesforce. Many apps I viewed have no packages. Users just install the app through their website. Should this be the approach that I take?
Packaging a Connected App is a legacy feature that was initially required in order to use them in other orgs. This is no longer a requirement, as the first time it is used in an org, it's automatically "installed" so that administrators can configure it. You don't even need a managed package at all any more for this purpose, as the Client ID that you provide during the authentication flow is sufficient enough to identify your app, display the logo, etc. The callback URL must match the callback URL provided by the calling app, or a security error will prevent the redirect.