Difficult to say without knowing how big your pots are and how low down in them the baby crowns are.
I like my asparagus crowns to be about 6 - 8 inches below the surface so that I can scrape the annual weeds off without damaging the asparagus roots, and I mound more soil over them as winter comes, to protect them. And even after 40 years, I am surprised by how far from the crown the ends of the roots are when mature - digging nearby I sometimes uncover them. So leave lots of space each side of your row.
Is this the best time to put them in? The usual time is March, but I suppose the crowns would be all right now as long as you don't disturb the soil in the pots.
Watch out for the asparagus beetle! They seem to appear from nowhere and lay tiny black horizontal eggs along the stalks; these become grey grubs that eat everything bare.
