Android Lollipop defaults to Mobile Data when Wi-Fi has not Internet access?

To extend on @ianhanniballake's answer, I've found that binding the network using ConnectivityManager.setProcessDefaultNetwork() prevents roaming and allows for full TCP access. Thus, within the onAvailable() callback you could bind the application process to that network rather than opening a connection to a particular URL.

ConnectivityManager connection_manager = 
    (ConnectivityManager) activity.getApplication().getSystemService(Context.CONNECTIVITY_SERVICE);

NetworkRequest.Builder request = new NetworkRequest.Builder();
request.addTransportType(NetworkCapabilities.TRANSPORT_WIFI);

connection_manager.registerNetworkCallback(request.build(), new NetworkCallback() {

    @Override
    public void onAvailable(Network network) {
        ConnectivityManager.setProcessDefaultNetwork(network);
    }
}

As of API Level 23: Please use the following OnAvailable Method:

@Override
public void onAvailable(Network network) {
    connection_manager.bindProcessToNetwork(network);
}

By default, Android 5.0 will only send network requests over networks that it detect have an active internet connection so while it may be 'connected' to the wifi, it is not going to send any data over the network.

However, the Android 5.0 APIs guide talks about the new multiple network support:

Android 5.0 provides new multi-networking APIs that let your app dynamically scan for available networks with specific capabilities, and establish a connection to them. This functionality is useful when your app requires a specialized network, such as an SUPL, MMS, or carrier-billing network, or if you want to send data using a particular type of transport protocol.

This allows you to build a NetworkRequest for a TRANSPORT_WIFI type and direct traffic to it via Network.openConnection() when you receive a onAvailable() callback if you must have certain connections happen over wifi even when the wifi network does not have internet access.

Android 5.0 provides new multi-networking APIs that let your app dynamically scan for available networks with specific capabilities, and establish a connection to them. More info here

So solution for you is ConnectivityManager.requestNetwor().