Each of them gets their own team/city and such, and suddenly they realize "Dear lord, I'm the only responsible one here!" Except it's by Batman's standards(i.e., wildly disproportionate to the entire rest of the world). Everyone else is perfectly responsible, they just aren't as hyperaware as the Batkids are used to being. No one but a Bat would walk into a room and count the exits unless it was a serious situation. No one but a Bat could look at a situation and formulate a serious game plan quickly, or see some small tidbit of information and be able to accurately predict where it fits in the greater scheme of things.
So the Batkids all step up to be the "responsible one" of their respective teams. They set the game plans, divvy up responsibilities because if they don't, then who will? And in doing so they each become the Batman of their team.
Dick adapts the best, being the eldest and having worked to keep others in line before. He's able to be chipper and spry while still being the Bat on the team. Jason? Well, he tries. But it's really hard to maintain good banter with subordinates in a crime ring when you need to make sure everyone is doing what they're supposed to. Tim and Damian? Forget it. Tim is always doing something to keep everyone moving, and Damian doesn't have the social skills to really make friends with new people anyway. They're really useful to their teams, no one disputes that, but they both run tight ships.
But when everyone gets back to Gotham, it completely different. They all know the parameters they're used to functioning in, the uptight, never miss anything, never stop planning ahead mindset that was drilled into them and that they drilled into themselves. Suddenly, they don't have to try and hold everyone around them to that standard so that they feel safe. They know the people around them, know that Dick counted the doors when they walked in, Jason saw any angles for covered gunfire, Tim made three different plans for if things went wrong an hour ago, and Damian had scanned for threats before the door swung shut behind them. They can trust the people around them to have their backs fully, because they all function at the same level.
The various teams get called to Gotham, and no one expects Tim to crack a joke and offer to wash the dishes for Damian so he doesn't have to go on patrol because since when does Red Robin let anyone do anything for him? Since when do Red Hood and Nightwing play chicken on patrol, jumping off of buildings to see who'll fire their grappling gun first, trading laughed insults the whole way down? Since when does Robin, angry and self assured, let someone else make the plan?
Over time, the Batkids learn what Batman did: that not everyone needs to function at that level to be good at what they do. It's okay for your teammates to be a little careless, a little clueless, a little unprepared compared to you. And, gradually, they start to relax. They still count the exits, sure, but they let the rest of the team function at their own levels. The reason they had to be as good as Batman in Gotham was because they were dealing with people who knew Batman and how to effectively counter him, anyone less adept than him would be the next best thing to cannon fodder. But most of the villains the teams go up against aren't from Gotham, and compared to people like the Joker they're sloppy, unprepared, and predictable.
The teams get used to more relaxed, more trusting Batkids. They'll occasionally make a joke, play a small prank, offer advice or a listening ear. Still a far cry from the almost irresponsible display they put on during family reunions, but they're part of the team now. Everyone knows that, behind those masks, eyes are scanning, always watching, always seeing everything and noting it down somewhere. But they become used to it, forget it's even happening most of the time, because the Batkids have stopped noting things aloud that they think are important, stopped trying to train everyone around them to be so hypervigilant. They can cover that base for the team, and the team can cover other bases.
It's still a bit strange, the next time the teams all meet in Gotham, how much more carefree the Bats seem. But not as wildly out of character as it did last time. Besides, everyone was able to stop some kind of small crime on the way to the meeting point, a rather large rooftop, and they're all comparing how many petty thieves and assaulters they caught on the way there. Nothing prepares the teams, though, for the Rogue Gallery to disrupt the meeting.
They didn't see them coming the few seconds ahead, like the Bats did, all leaping out of the way and expecting their teammates to do the same, forgetting who they were for half of a moment. The individuals team members all merge together, used to working with their own teams and able to muddle through working with the other ones, but it's the Bats that get everyone through. Inside jokes are tactical commands, smiles and winks are directions on who to strike, the banter that seemed almost too childish for these uptight, no nonsense people is their primary weapon. Nightwing and Red Hood dive off the roof to avoid an explosion, waiting for the last moment before launching their grappling hooks and swinging back up. Red Robin trades Two Face for Poison Ivy with Robin, who lets Batman direct him on where to strike in a very few words.
The Bats work like a well oiled machine, working their hardest to keep everyone less adept, less aware, less prepared in the loop, calling out the smallest of openings as they see them and some of them are truly miniscule, called one moment, appearing the next, and gone before they could blink. But the Bats manage to hit those tiny openings, aiming form them before someone else can signal they've been spotted.
It takes a little while, before the Rogues are taken care of and medical help is administered. But the Batkids are already back to joking, laughing with one another as the teams try and recover. Red Hood playfully punches Robin in a bullet wound on his shoulder, and Robin kicks the large gash on his shin in return. Batman stands off to the side, sighing and shaking his head as his children mock each other for sloppy work, missing openings, getting hurt. Even joins in, when Nightwing makes a comment about him not dodging Flash getting thrown into him. The teams just watch on because was Robin seriously critiquing Nightwing on his seemingly perfect backflip? What did Batman mean that Red Hood's feet crossed somewhere in the fight, how had he even seen that? Why was Red Robin apologizing for a "messy" plan that had kept everyone alive?
The Bats, everyone concluded as they were stitched and bandaged, were just built different.
