does using tiptronic transmission save gas?

Tiptronic is a trade name for advanced auto transmissions used in some car brands. It includes the torque converter, so its fuel economy shouldn’t be extraordinary, like that of the VW Group’s DSG (double-clutch gearbox, a converter-free efficient automatic transmission installed even on some Ferraris).
However, you can do a lot to burn less fuel by adopting and/or changing some habits – cruising at constant speed, selecting comfort gear-change setting, if available, keeping your tires slightly overinflated and the car in good shape, getting rid of any trunk junk. Let the transmission do its own shifting. In auto mode, the selector may be in any position, it will shift up to that gear, which is why the highest should be selected in most (normal) situations. If you use paddles or shifter to shift yourself, shift up early and shift down late, except on downhills, like with a normal manual transmission. Try to make the engine work below and up to its max torque. Avoid fast acceleration, especially uphill.
Yes, engine braking saves both gas and brakes, especially in engines equipped with fuel cut-off valves (most recent ones).