It really should't matter when. One certainly should be able to put the mature media right in (and I agree, put it such that the water flow goes through it first and then into your virgin biomedia, like your sponge)...
And yet, for myself, I kind of like the idea of loading up everything -without- the mature media and running it a day or so just to see that everything is funtioning and to let the new tap water age a day or so and when everything seems fine then get that mature into the correct position in the stream sequence inside the filter box. It's good not to disturb the mature media more than you have to since the biofilms to have some structure to them, albeit microscopic.
Using mature media is quite reliable, but its good to understand from the outset that moving media always carries the possibility that you will somehow kill it. Sometimes it just doesn't survive the disturbance and there may be no clear reason why, its just the way it is sometimes. But the vast majority of times it works like a charm.
WD
