A standard 8’ x 8’ hot tub weighs about 5,000 lbs when fully loaded with water and people. Needless to say this is much more than a typical deck frame is designed to support. You will always want to build a separate frame within your deck to support a hot tub. Adequate strength for this application is only achieved by installing properly sized footings below all the corners of the hot tub. You will want to get the exact specifications for the hot tub including the size and weight when filled with water before making considerations about how to support it.
Many builders choose to set the hot tub at a lower elevation than the surrounding deck allowing a person to step down into the water with less bending and climbing. Always make sure you plan ahead to provide access to the controls. If your deck is being built near the ground you may consider setting the hot tub on a poured concrete slab with access to the deck. Never place a hot tub on top of a deck that was not specifically designed to handle the intense loads.
Be sure that this design is acceptable by your local building department before you attempt to build it.