"Tarnation" is an example of a minced oath or euphemism which is where an alternative word is used to replace a word considered to be offensive. Typically, the user and listener are both aware which word is being replaced so the force of the original word is retained while the religious, sexual, or scatological offense is not given.

Tarnation and Darnation are both replacements for the word "Damnation" which is still used as a form of that phrase (ie "What in Damnation") although Tarnation may have been influenced by the word "Tarnal" dating from the same period as a shortened form of "by the Eternal" meaning "by God".

The word appears in American English from the early 1780s. This is more an etymological question than history.