With both the current system and the National Popular Vote approach, all counting, recounting, and judicial proceedings must be conducted so as to reach a "final determination" prior to the common nationwide date for the meeting of the Electoral College. In particular, the U.S. Supreme Court has made it clear that the states are expected to make their "final determination" six days before the Electoral College meets.
Existing federal law (the "safe harbor" provision in section 5 of title 3 of the United States Code) specifies that a state's "final determination" of its presidential election returns is "conclusive"(if done in a timely manner and in accordance with laws that existed prior to Election Day).
The National Popular Vote compact is patterned directly after existing federal law and requires each state to treat as "conclusive" each other state's "final determination" of its vote for President. No state has any power to examine or judge the presidential election returns of any other state under the National Popular Vote compact.