They're closed up in Jack's office for some privacy as they "have a talk". It's more like a way to mute some of their volume when they get into it, but they don't stay loud for too long. Jack snarks back at her, in the way only friends can really get away with; you have to actually form your thoughts and pay attention when you type, and you don't end up with the ramblings of recordings or videos, and going through it actually helps commit it to memory instead of recording and forgetting about it... (Of course, he's the first to groan about how much paperwork he ends up doing, but that's bureaucracy getting in his way, right?) "Typing, old-fashioned? Please, you grew up with typing! You weren't around when all this was done with fountain pens, and then typewriters..."
When he's about to go off on a tangent about holovids and Thought-Mail, she draws his attention off their friendly bickering. "Hmm, what's-- whoa?"
With the camera's angle, he can't miss that Ianto's hand is in the Doctor's-- but it's less clear when Ianto leans in just how close he gets. It might just be Jack's wishful thinking that there was a kiss, and he automatically starts keying in the commands to record a backup of that and continue recording. This is looking very intriguing, and he doesn't want to risk any of the automatic data dumps losing it. He gestures for Rose to pull up a chair.
The corridors through the Hub let the Doctor and Ianto bypass running into Jack and Rose as they head into one of the lower levels. Jack hits another key and the monitor fills with that feed, and tracks from camera to camera whenever the pair move to the next one's range. Once they reach a cozy room set up down there, the feed settles in there and Jack helpfully zooms to be sure he and Rose don't miss anything. "Now what do you suppose they're up to down there? And did I see what I thought I saw?"
Reposted with corrections thanks to scribe misremembering sequence of events. Her punishment for her failure will be lightened thanks to realizing she needed to fix it. Due to the coffee retrieval, scribe has sneakily put Rose and Jack in the office so they won't be noticed during that break.