The FBI isn't typically allowed to do that without a warrant, which would require probably cause. They or the NSA could do it anyway, but the evidence would never be let into court.
The most likely answer if they got emails from whoever they were sent or forwarded to.
Chinese spies looking for this information would, presumably, pose as experts or students and get involved in academic discussions at conferences and email chains/listseves.
So hypothetically the FBI could bust a real spy, then see emails from Dr. Xi sending technical information and they suspect the worst.
The FBI could have even infiltrated these groups themselves directly, which doesn't require a warrant or any oversight.
One other way I just thought of is that public school employees, like Temple, don't own their work email. A regular person can use FOIA to get professors emails. I wonder if the FBI is allowed to use FOIA.