So you mean tell the kids that they’re really “minding” the 3k for the OP but if anyone asks, say it’s a gift?
I think they’d need to be quite dim not to realise that the money was really theirs.
As I understand it, Jamie's intention is to deposit 3k into each kid's account each years, telling them that they are to mind the money for him and not to touch it, and that if there are any tax consequences or liabilities he, Jamie, will bear them (which is of course consistent with the money being Jamie's, and not the kids).
Remember, the only reason that Jamie says this to them is because he doesn't want them to have the money — he doesn't trust them to deal wisely with it; he doesn't think they should have control of that kind of money, and responsiblity for deciding what to do with it, until they have a bit of sense. So the money isn't "really theirs" at all. If Jamie wanted it to be really theirs, he would just give it to them. The restrictions he's imposing on the money are intended to be real, not fictional. If there's a fictional element to this, it's putting the money in their accounts, to create the illusion that he's giving it to them, when in truth he's doing nothing of the kind.
The kids won't think, at the time each 3k is given, that the money is "really theirs", because it's really not theirs. Jamie has been explicit; they're not to touch it. It's Jamie's money; they're to mind it for Jamie. At most, they might hope that some day it will be theirs — that Jamie will tell them they can have it.
So, the day finally comes when their dreams come true and Jamie, in his wisdom, decides to give them the money. So he says "this is all yours now".
That's when the gift is made. It's a one-off gift. And it's for considerably more than 3k.
(There may still be no tax liability. They're Jamie's kids, and they can each get up to 400k from him without incurring any CAT liability. But the entire charade is completely pointless unless Jamie thinks there is, or is likely to be, an actual CAT liability on the aggregate amounts he expects to pass to his children, so I'm discussing it on that basis.)