I think they were spooked for good reason.
So the two senators had an interaction with a spy/assassin with one being the target.
Mon was under constant surveillance and having multiple spies as drivers/security for her.
Draven was still in the process of turning the militia into an army, but he no doubt heard about the imperial spies caught and killed (Will was there)
So the members of the leadership group all had recent interactions and stories of espionage, while knowing that their espionage wing under Luthen collapsed, with some of the remnant members being undisciplined and still operating like freelance agents. A lot of time had passed since the heist, as they are procuring ships and x-wings they probably overlooked the importance of those initial funds. But I think Cassian taking the cue from Draven to not attack the other member who questioned him/Luthan also signified a change in their relationship and trust. I think Draven likely vouched for him, Mon, did so as well, and Organa was reminded what Cassian did and the costs he paid. I think that is why Bail told him.
I also like how the force sensitive healer stared Cassian down with a disturbed look. I think she sensed his fate in that moment.