CNN is reporting that the information comes as a brief entry in a docket between 6:30 PM and 7:00 PM on a Sunday.
The timing indicates that there's a "sense of urgency" about it, possibly to get it on the record before the Trump family takes the stand all week in New York, where you know there's going to be hallway commentary multiple times a day.
Stricter? I don't think it's likely that the scope of Chutkan's gag order will change. It's possible that the scope will be more specifically clarified. The real question is whether Chutkan will modify Trump's conditions of release to include this gag order. That should happen, so that when he violates it, the law states that his pre-trial release is terminated.
Note that I said "the law says" and not "he will go to detention pending trial." Because no matter what anyone says, he will never see any real consequences for anything he ever does.