Who on earth told you that Tempo doesn't matter. You can find the correct Tempos by going to Dancesport USA. U.K. or Dancesport Australia. Any Dance music recorded by the leading orchestras will be correct. A Foxtrot for instance will be played at 30 Bars per Minute with a 4 Bar Introduction. From there on it will be 8 Bar Phrased. Think of it this way. Each single page of a book represents one bar of music, There are Eight pages to each Chapter. There are usually Eight Chapters on a disc. Which is of course 64 Bars of Music. Each bar of music has four beats. The Waltz has three and is played at the same Tempo as the Foxtrot.
Latin. If this is played too fast the first thing that would go is the correct movement of the hips. Rumba is 25 Bars per Minute. This is only the beginning. There is a lot more than meets the eye in understanding correctly played Dance Music. If you don't understand what dancing in Rhythm as well as dancing in phrase means. Then find out.