Whatever they like. For the most part I would imagine the majority of a carbon dividend would go on making their lives less marginal. Maybe a nicer home near a decent school, better appliances, or clothes. Maybe some savings. Once they have, perhaps they will look to accumulate more emissions like their more wealthy peers.

So long as the nett overall emissions are down and decreasing it matters little. You ensure that by setting the rate of the carbon tax high enough. Perhaps an accumulating rate.