Make Fios router my DEFAULT router on MacBook

Is the FIOS router providing DHCP services? If not, then what is?

The DHCP server needs to provide the default route to your clients. In case your DHCP server only accepts options, the default router is option 3.

 

Take a look at the screens below:
a) do you have the item for "Ask to join known networks" marked?
b) is your FIOS router network name first on the preferred networks list accessed by clicking Advanced with the AirPort connection highlighted in your Network system preferences? If not, you'll want to drag it up above whatever else is listed there or delete the preferred networks that you don't need the computer to auto-connect to any longer.

 

Open your Network Prefs. It should show the DHCP server for your connection. Is the DHCP server IP the same as your FIOS router IP?

EDIT: Now that I read this differently, the above post may be more what you're after. So you're saying your Mac connects to some other network first instead of your new FIOS router?