Adding a taxonomy term translation changes the original language value! I have an issue when I try to add a translation of a taxonomy term using the site UI. The original language value changes to the translation value that I added.

How can I prevent that from happening?
You need to make sure it is translatable in the language settings.

Go to:  

/admin/config/regional/content-language

Make sure that taxonomy term is checked in the custom language settings.  If not, check and save.

Then find the Taxonomy section in the form.  In this section, make sure that your vocabulary and fields you want translatable are checked.  Include the show language on edit option as well

Once you have done that, go to:

http://www.solarwindsmsp.test/admin/structure/taxonomy

And create translations for the vocabulary for each language you want.

Also edit the vocabulary settings and make sure there is a default language specified for new terms.

Next, if you have existing terms, you need to edit the term and set a default language in the dropdown.  E.g. english instead of not specified.

Once you do this, you will get a translate option on the edit / delete dropdown in the list.  Select translate to add additional languages.