The explaination is correct as I understand it.
The put (or call) is in-the-money when the price is passed.ie 12.50 put is in the money when the price is lower than 12.50.
The price you pay is the premium in this case 20c.
For you to be in the money all you need is the buy price to be above 20c.
Don't get confused with the lingo.
