This isn't a client method for achieving this, this is a server method. So apologies if this isn't what you're looking for.
I can't say that this is the best way, but you can use the 'CustomACDPostAlertInteraction' customization point to call a custom handler (use query media type to filter out non callbacks and perhaps other logic if you need to filter out specific workgroups). You can then use the User Login List tool to get the station of the agent and then the Place Call tool to place the call for that queue.
If you want to filter this by user, you might use a custom attribute on their user profile that you can query with Get Ds Attr. This is roughly how we achieve an automatic outbound call on callback assignment.