Now that it's out, this can be answered definitively.
In DoAD, you can perform combos the old-fashioned way, or by tapping it on the bottom screen. If you're playing with buttons, the bottom screen highlights your combo sequence(s) as you enter the commands. Overall I find the user interface much nicer than Street Fighter's.
Unlike Street Fighter IV, there is no segregation between touchscreen / button control in online play. If someone is entering commands with the touchscreen an icon pops up on their side of the screen, so you know if they're doing it, but you can't forbid it like you can in SFIV. Realistically this probably doesn't matter, but some portions of the Internet are up in arms about it.