yes, I do have a problem with it. (And just as points of fact, SCOTUS ruled while the tribunal was ongoing, the defendants were convicted after the ruling, and evidently two of the defendants were American citizens.)
As you've been already told, that decision is legally controversial. The SCOTUS, in a hastily arranged special session, issued a statement of their decision within a day after hearing 9 hours of oral arguments and then spent three months cobbling together a written opinion (the actual legal justification) for its decision. Yes, that's correct: the SCOTUS made its decision before it had determined and agreed upon the legal basis for such a decision. Considering that 6 of the defendants had been executed over two months before the court released its written opinion, it's no great surprise that the SCOTUS, despite some concerns within the court regarding issues the case raised, rendered a legal justification supporting what was already a fait accompli. The SCOTUS acted as little more than a rubber stamp to the Executive and the military and then put together an opinion to justify itself.
Furthermore, FDR issued the proclamation directing a military prosecution in this case not because the case was nonjurisdictional to the Federal judicial system (the case was indeed jurisdictional to the civilian court system) but due to expediency and a desire to ensure a specific outcome. Others who were arrested and charged with aiding the saboteurs, however, were tried in the civilian court system.
Additionally, some of the legal circumstances that existed when FDR issued his proclamation and Quirin was decided have been superceded by subsequent changes in Federal criminal law and other court decisions.
Subsequent Administrations' practice (until that of George W. Bush) was to prosecute terror suspects under Federal civilian criminal law. (Even the Reagan administration prosecuted terror suspects in civilian court.) GW's administration as we know sought extralegal, extrajudicial and in fact illegal means of doing what it wanted in a variety of areas. It cited the questionable authority of the "unitary executive" (aka, "if the President does it, it's legal") as a basis for its actions. In this instance it also proffered the dubious Quirin as its legal authority. Although the Bush Administration also wound up trying terror cases in the Federal court system.
You cite Quirin. Another FDR action upheld by the SCOTUS (Korematsu v. United States) was Executive Order 9066 which was used as the legal basis for the rounding up and internment of Japanese Americans (as well as to a significantly lesser extent, some German Americans and Italian Americans). That executive order was not rescinded until 1976 by Gerald Ford. The constitutionality of FDR's order also has not yet been explicitly overturned by a subsequent SCOTUS ruling. Would you now support a similar action by a President since a previous SCOTUS ruling said it was OK?