Stoinis, playing for Southern Brave against Oval Invincibles, was rushed by a Hasnain short ball clocked at 88mph/142kph and caught at mid-off during Brave's seven-wicket defeat on Sunday night.
When he was walking back to the dugout, Stoinis mimicked a bowling action with a throwing motion. ESPNcricinfo understands that Stoinis was spoken to by match referee Dean Cosker but that he will not be formally charged with a breach of the ECB's disciplinary code.
Hasnain was suspended from bowling after being called by umpires during the BBL, but was cleared to return in June after remodelling his action. During that tournament, Moises Henriques had similarly questioned the legality of his action shouting, "nice throw, mate," after playing and missing.
Hasnain has taken three wickets in three appearances for Invincibles to date, with an economy rate of 1.93 runs per ball. His action has not been reported by the umpires in any of those three matches.
Invincibles' win on Sunday was their third in a row, and leaves them well-placed to qualify for the knockout stages.