BBCA can actually handle both what are described as traditional push and pull mechanisms. In general, the majority of the functionality is initiated from the client as this is the only way that you can reliably manage a mobile workforce that only periodically connects to the network (or even desktops that are turned off regularly).
Hence inventory requests, policy requests and patch requests are initiated from the client and then it connects back to the core transmitter infrastructure to find out what it needs to download.
The deployment manager functionality allows you to to push requests out imediately from the core infrastructure (provided that the clients are all on and connected to the network). To do this it uses the tuner admin port on 7717 by default, so this will need to be open through any firewalls.
Can't really add much to Paul's answer, but whilst the core technology is definitely pull (even the deployment manager is a push-initiated pull), the administration method is more push. A central group of people dictate what gets "pushed" to the clients, despite the technical method of delivery being a pull!