Why did they blame Moshe and Aharon for killing the people? They sinners caused their own death!
Da'as Zekenim, Hadar Zekenim: You should not have tested them with the Ketores, through which Nadav and Avihu died. Rashbam - indeed, Dasan and Aviram deserved to die. They complained about the death of the 250 men. Ramban - Hashem did not command so; you chose it of you own accord! You should have used the stick or some other sign [to show who is proper for Kehunah].
Ramban #2 (citing Ibn Ezra): The tests that Moshe made did not prove that the tribe of Levi and Aharon were chosen 1 - and in all probability, Moshe caused them to be burned 2 with his Tefilos or via some other Chochmah.
Ramban #3: Although the people believed all along that Aharon was the chosen Kohen Gadol, 3 they wanted the Bechoros to serve in the Mishkan in place of the Levi'im, 4 having rejected the switch which, they claimed, Moshe made of his own accord. Consequently, they now accused Moshe of having chosen the Ketores, which did not prove that the Bechoros were not eligible to perform the Avodah of the Levi'im. 5
Seforno: 'You should have tested them with a Korban that many Kohanim may perform simultaneously, and not the Ketores, which only the Kohen who offers the Olas Tamid may bring'. 6
Hadar Zekenim (16:5): You should have given to them Kadosh incense pans like yours.
Ramban (according to the Ibn Ezra): They did not believe the outcome of the test of Ketores at all, as is evident from the test of the sticks later, on Pasuk 17.
Ramban: They did not question the punishment of Dasan and Aviram, which was by Divine Decree, as hinted in the previous chapter, Pasuk 24.
Ramban: Since they had seen how fire had emerged from before Hashem and had consumed the Korbanos that he brought.
Ramban: So that all the tribes have a share in the Avodah.
Ramban: Which explains why, in Pasuk 23, Aharon's stick sprouted blossoms on behalf of the tribe of Levi.
I do not know his source for this. There was a special lottery for who will offer Ketores (Yuma 2:4). It was not limited to those who offered the Tamid! (PF)