I stumbled on this thread a while back ago and it has been bothering me. While you intentions are good..trying to describe how to tan items, you are misinformed about some of the chemical processes involved. I have been doing taxidermy and tanning for 27 years.
While using borax has its place in preservation qualities. It is caustic and will cause hair to slip the way you are using it here. Skip the borax step. Rinse your hides in regular water before adding to your pickle that you are making with the alum.
For your pickle, in the steps you describe, it has you mixing alum--an acid, and baking soda--a caustic, together. Of course your going to get a chemical reaction of fizzing. You are neutralizing the acid. You need to keep the acid at a pH between 2 and 3. Even 3 is somewhat high for tanning. I personally like to keep it below 2.5. After the hide becomes white from being in the pickle or tan as you call it, this will occur in a few days, then you can neutralize the hide with the baking soda solution.
If I were to use household chemicals to tan a hide with the hair on, this is what I would do:
Flesh hide
Put hide under salt for a couple days
Rinse out hide with water to get excess salt off
Mix Pickle or Tan in this case, adjust amounts equally enough to submerge hide, this will bring the ph to about 2.5
use the 5% vinegar found in the grocery section
2 Qts. of White Vinegar
2 Qts. of Water
1 Lb. of Salt
Let soak for a few days
Take hide out of pickle and drain letting it become damp dry, do any final fleshing at this time to get any remaining meat and fat off.
Place back in pickle for another day.
Take hide out from pickle, drain, and place in enough clean water to submerge with 4 ounces of baking soda
This will neutralize the vinegar. Let soak for about 20 minutes. Agitate every 5 minutes.
Take out hide and once again rinse in clean water.
Let the hide dry until it looses about half of its moisture.
Oil with neatsfoot oil, but try to find the bisolfianted (sp) or
Go to the drugstore and get some lanolin...this is also known as wool oil. Heat this up until its a liquid and apply to the hide on the flesh side only. Just use enough lanolin that the hide will soak in. The hide will also need to be somewhat worm also
Let the hide dry , working it as it is drying to keep it soft. You can use sandpaper to give the hide a velvety swede feel.
There you have it. All these steps are chemically compatible with each other.