The term "Up and Adam" is a misused phrase of the proper term "Up and at-um".
The phrase "up and Adam" is often used who are not familiar with the origin of the terminology. The correct term (up and at-um) seems to have originated from the great war (WWI) of 1914, when the troops came up out of the trenches to advance on the enemy. The cry "Up and at 'em boys" would have given the troops encouragement. Likewise, the phrase "up and Atom" is also incorrect use of the term.
"Up and at-um" boys, was a battle cry to have men advance out of the trenches during WWI. Not "up and Adam" nor "Up and Atom".

Cite:
American Psychological Association (APA):
up-and-at--em. (n.d.). The American Heritage® Dictionary of Idioms by Christine Ammer. Retrieved November 10, 2015
Chicago Manual Style (CMS):
up-and-at--em. Dictionary.com. The American Heritage® Dictionary of Idioms by Christine Ammer. Houghton Mifflin Company. November 10, 2015).

Modern Language Association (MLA):
"up-and-at--em." The American Heritage® Dictionary of Idioms by Christine Ammer. Houghton Mifflin Company. 10 Nov. 2015.

Institute of Electrical and Electronics Engineers (IEEE)
Dictionary.com, "up-and-at--em," in The American Heritage® Dictionary of Idioms by Christine Ammer. Source location: Houghton Mifflin Company. Available: BibTeX Bibliography Style (BibTeX)

title = {The American Heritage® Dictionary of Idioms by Christine Ammer},

month = {Nov},

day = {10},

year = {2015}
by Agent0092 November 10, 2015
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