iMessage on older MacBook Air

I have a MacBook Air with a recent (last night) update to the OS X El Capitan Version 10.11.4. 1.7 GHz Intel Core i5. 4GB.

I have been excited to try the iMessage feature on the update with my iPhone 6S Plus but I cannot seem to get it to sync. I have gone into the settings of iMessage and I'm assuming the Preferences are in favor of the app working but I'm getting nothing. I can send messages from the iMessage app on my computer to people who are in my contacts but it does not show up on my phone as a continuous conversation (no before or after, or during if I switch devices).

Thank you for your help!