Hey Grymm428, you have correctly interpreted the rules. When you learn a new spell domain you automatically become proficient with 2 spells from that list.

• A level 1 mage starts with Arcane Magic and can choose to be proficient with two spells from this domain. If they pick Form Magic as their other class ability then they can pick two more spells from the Form domain.
• When they reach level 2 they can pick 2 spells to be proficient in from any known spell domain.
• If they learn a new spell domain (new class ability say Earth Magic) then they automatically become proficient in 2 spells from this list.

Hope that clears it up for you.