When and how does combat start in a standoff?

I run Adventurers league at a local game cafe with a veteran group that has lots of experience playing prior editions. However these players knowledge of the rules is an amalgamation of 5e rules and previous editions’ rules, so we’re never quite sure if a specific rule belongs to 5e or not.

The question I have is in the following scenario, when exactly does combat start? Are ‘readied actions’ valid in this scenario and how do they interact with the 5e initiative rules?

I acted under the assumption that combat starts when the first creature decides to take a hostile action, rather than just threatening to do so–however this may have been too late.

The PCs were involved in a standoff with a group of bandits. Both sides came upon each other unaware. We didn’t roll initiative since although everyone was on edge, no one wanted to initiate the fight. Perhaps we should have rolled here but I know these players take ‘roll initiative’ as ‘roleplay is done just kill everyone’ and I wanted to build some tension first.

Most of the players told me they’d shoot if the enemies made any sudden moves. After a couple minutes of heated negotiation I decided combat began when one of the bandits got jumpy and was about to shoot on instinct. I decided the jumpy bandit didn’t surprise anyone, and since positions were already determined on a grid, I called for an initiative roll. I decided that the bandit with the highest initiative was my ‘jumpy’ bandit. When none of the PCs beat his initiative his turn started and he shot one of them.

At this point a few players shouted they had readied actions to shoot the first person who acts, so they should get to shoot now (before the bandit, using their reactions) and take their turns later in the round.

I honestly didn’t know how to respond to this for a moment, but then I just said “It’s a standoff, everyone’s ready to shoot the first person who moves. That’s why we’re rolling initiative–to see who reacts fastest”.