How should I add the soon to be new substrate?

You are worrying too much about adding the substrate.

What kind of material is ADA Am....soil II and/or Fluorite?

Is this a material that has lots of iron added? Iron additives would make your water turn red/brown...not good. If yes, then you need to go to plan "B" (removing fish, water, ornaments usw.) in order not stir up the reddish iron additive.

If the material is not clouding the water, then I would rinse the new gravel and add it cup by cup into the tank. The fish would stay out of your way, and you should be able to get your substrate into the water without making a mess.

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MY TANK SET UP PROTOCOL FOR NEW TANK:

Set up for my 7 planted tanks has always started from the bottom up.

1. First I would mix my iron containing substrate with some gravel and place it in the empty tank on the bottom.

2. Added clean (rinsed clean) gravel on top of substrate and plant my plants according to a plan (set up earlier).

3. Add water slowly so nothing gets stirred up or plants get dislodged.

4. Add plant fertilizer according to recipe.

5. Using some dirty filter material from a previous setup in the new filter, I established beneficial bacteria to start cycling the tank. This takes some time - sometimes some weeks - but you need the beneficial bacteria in order to add "some" fish slowly (not an army) to the tank.

6. Don't be in a hurry and READ about tank cycling - this will really help you. Get yourself some good aquarium books.

If you leave the water in the tank while adding the substrate, you'll likely end up with a soupy mess of sediment. Short of scooping cupfuls of substrate (which I'd recommend rinsing first, if you ever want more than 3 inches of visibility in your tank) straight to the bottom of your tank, and gently spreading it out, you'd do best to drain the tank to about 2-5" of water. The fish will be fine in a bucket during this time, especially if you move the filter onto that bucket for the duration of the scaping. To fill up the tank, gently pour water onto a decoration, so as not to stir up all the latent sediment lurking at the bottom. Just after this, vacuum the gravel to remove all that excess, then feel free to re-acclimate your fish.