They are still filming, at least for another several weeks. Jamie's been VERY quiet on Twitter, but… he's Jamie. ;) There's still an element of being stunned that he's on Twitter at all! Kerry's also been a lot quieter overall while they were on their holidays over there, and that's totally understandable. When Kerry mentioned visiting the set with the kids, I did take the opportunity to tweet them that it would be great if Jamie would post updates from on set from time to time… which I was very hesitant to do unless the opportunity presented itself, and I won't do it again. (Didn't get any responses.) I don't think there's any point in asking about it more than once, but it felt like it was worth a shot to put the notion out there.
I don't expect he'll ever be as casual a hand as some actors are at tweeting what they're up to, it's just not really who he is. But at the same time now that he has it, it would be smart of him to keep people updated on what he's working on; he probably just still needs to find a level he's comfortable at. I will say this, though, I do wonder if you're right and Sky is deliberately trying to keep a lid on the show overall; some of Jamie's co-stars are also on Twitter, and though they've occasionally tweeted about the show it's always in the briefest terms and they never post photos.