1. Exposition

How would the adversaries have heard of the exiles' building of the temple?

Ezra 4:1 (ESV)

1 Now when the adversaries of Judah and Benjamin heard that the returned exiles were building a temple to the LORD, the God of Israel,

At the end of Ezra 3, the people of Israel gave a loud shout of joy together with weeping when they saw the foundations of the temple being laid. Ezra 3:13 tells us that this sound was heard far away. Presumably, the people living in the areas around Jerusalem heard this sound and came to investigate what the Jews were doing.