Yes, Padilla was indeed caught on American soil, as were the 7 Hitler-leaning American citizens who were caught during World War Two after being sent back from Germany on U-Boats in order to conduct sabotage against us here.
Acts of sabotage reclassify civilians into enemy combatants, subject to the Geneva Convention, which means that we can execute instant battlefield judgement on them, up to and including summary execution on the spot, without any form of trial whatsoever.
Likewise, we can shoot *all* enemy combatants on sight without trial, even if some of them happen to be U.S. citizens (Taliban Johnny comes to mind from Afghanistan).
Once one decides to actively wage war against the U.S., one shouldn't be surprised to see our ordinary protections save the day for said deeds. We aren't going to stop a battle, even here in the U.S., in order to give somebody a trial by jury. In war, we shoot those who oppose us. War is a brutal thing, and certainly a last resort, but nonetheless, there are those who would choose to force their views onto us via a path of war and terrorism, leaving us little choice but to respond overwhelmingly.