He stopped the summoning from coming up. Even if he didn't, Minato soul was still trapped in the Reaper giving an empty coffin had it not been stopped.
Thing is even orochimaru at that time don't know the fact that Edo tensai can't resurrect some one who is sealed in death god's belly so he researched it after and found a way to summon and release them from death god. Third hokage just assumed that he stopped it.
No, it was just a retcon. Back then, Kishimoto didn't have the same concept of Edo Tensei as in the war arc.
Remember, we have seen how it works when Kabuto showed the jutsu to Tobi.
Before there is any coffin, the body is created with a ritual. The coffin comes later, to store the bodies until they are summoned.
Here is the panel:
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At this point, the ritual of Orochimaru already must have failed as far as we know, because Minato's soul could not be summoned out of the reapers belly to create a body made of dirt.