Here are some other recent NY Times headlines that use the word fallout
Trauma May Have Fallout Over Generations
Cambridge Analytica and Facebook: The Scandal and the Fallout So Far
As Trump Struggles With Helsinki’s Fallout, Congress Faces a New Charge: Complicity
Inside Uber’s $100,000 Payment to a Hacker, and the Fallout
Nissan and Renault Wrestle With the Fallout From Carlos Ghosn’s Arrest
Fallout is widely used to mean "affect-effects" with no secondary or tertiary connotations.
I mean....you really thought there was some kind of nuclear disaster in Helsinki after reading that headline?