The exact history of the conga drum seems to be a bit misunderstood. I've read various articles that seem to point to either an African or Cuban descent. However one thing is sure: that the name 'Conga' is actually used incorrectly in the U.S. In Cuba, where these drums were developed, the word conga is usually only applied to a drum and rhythm played during Carnaval (or Mardi Gras in the U.S). A more accurate term, used in a traditional sense and by most Spanish-speakers, is tumbadora. This term is not traditionally applied to the drums played in Carnaval, but for those played in most traditional and commercial Cuban music.
According to Nolan Warden's brief history on the Conga drum, Cuban rhythms were picked up and popularized by the U.S. media in the early to mid-1900's when people were freely traveling to and from Cuba. This led to many U.S. pop-culture explosions of "Latin" styles, one of which was la conga. Even today, a watered-down version of the la conga rhythm isn't hard to find at public gatherings throughout the U.S. This and other pop-culture use mistakenly led to the word conga being used to refer to all Cuban drums of similar construction.
The word tumbadora, which is considered more accurate among Cubans and aficionados, comes from the folkloric style called rumba (not ballroom rhumba). Since rumba is considered to be responsible for the musical development of these drums, the word tumbadora is used out of respect for that setting as opposed to conga, which is a more commercial term. Today, it's not really necessary for English-speaking percussionists to call these drums tumbadoras. Congas or Conga Drums works just fine!