Now I avoided what has been mentioned in the article to deploy contracts, where you can download the default Mist and start it using your private network, this will make deploying your contracts easier (using third new Terminal:
You should see your first account full of ethers :). Enjoy!
Another thing worth to mention her, after you deploy your first contract using Mist, you need to go back to your second Terminal (where you are inside the node) and start mining again, otherwise, your contact deployment transaction will not be processed:
miner.start(1)
Check the Mist, and make sure that the transaction at the bottom of the screen already processed, then you can go back and stop mining:
miner.stop()