Correct spelling, explanation: tandem is a noun that originates from the Latin tandem (meaning at length [of time], at last, so much). This word is spelled exactly like the Latin version and there is no reason why we should change the letter -e into -u. Therefore, the only correct form is tandem, not tandum.

Definition of tandem:
noun, a formation of people or animals, one behind the other
They moved in tandem and didn’t even look at each other.
We ran in tandem so as not to disturb others.

Idioms with tandem:
One of the most commonly used idioms is: in tandem (with somebody/something).
Two marketers worked in tandem with our plans.

Incorrect spelling, explanation: there is no reason why someone would write this word with the ending -um and not -em. The original noun comes from Latin, and we have to look at its roots while spelling. The mistake may occur because the suffix -um is associated with the Latin language, but the only correct form is tandem, not tandum.