You don't have to tip anyone to make a reservation!
The Odyssey is the Alternative dining room - you will be assigned a table in La Fontaine. If you want to eat in the Odyssey, I would suggest you check your daily program when you board the ship, see if there is mention where & when to make reservations and then do it. Depending how full the ship is and how busy they are in the Odyssey, you may only be able to reserve for one night.