Was just going to make the same point about the tarp/footprint needing to be under the fly. Most modern tents do have a waterproof floor so unless yours isn't, I might even omit the tarp/footprint in order to get the tent up faster. Footprints while they do provide an addition water barrier are largely to stop abrasion by keeping the dirt and pointy things away from your tent allowing the floor of your tent to slide over the footprint rather than grind on a rock...generally less of an issue when it is wet...but it is a judgement call. I have always used a footprint.
Some 2 wall backpacking tents have a "fly first" feature which used the footprint so obviously in that case you might use the footprint to get the fly up before assembling the rest of the tent. My tent has this feature but I have never had to set up in heavy enough rain to warrant using it. Doing it in rain gear seems like it might be counter productive...a better use of it is a "fly last" take down if you have to pack up in the rain.
Another aspect of this is that well used campsites tend to compress and hollow creating a potential puddle. If you don't have a choice of site you might dig a small channel to ensure the water does not accumulate. Having an emergency shovel along helps. Obviously there could be problems with this depending on the kind of site so use your judgement and don't dig up the lawn.