Rhythm and tempo are two distinct concepts in any language. Rate and tempo (and pace) are synonymous. Rate and rhythm are not. If you speed up a musical performance, you will have a faster tempo, but the same rhythm (which refers to groupings of beats, relative relationships of note durations within a particular rhythm, syncopation, placement of stress, etc.). The same concepts are present (though usually with less precise measurements) in spoken language.
Some places pronounce the first R or rr the same as the J in Spanish. My entire family is from central Puerto Rico (specifically a very rural area within the Cordillera Central), and that's how they pronounce it. So ritmo would sound like jjjjitmo, with a very hard English H sound. My grandfather's name is Ramon, but my grandmother calls him jamon, which coincidentally means ham in Spanish. It confuses people.
In the lessons, "r" as the first letter of a word, always sounds like "dr" to me so that ritmo is pronounced dritmo. For me, it is difficult to get the rolled "r" started when it is at the beginning of a word and I suspect that native speakers do it when they are trying to speak clearly
And "r" after "n", "m" and "l" is always rolled, unless you have a problem and you can't pronounce it (there are many people, even native Spanish or Italian, Bulgarian... speakers). I learned how to pronounce "lr" - when you pronounce the "l" (like in "le" "li") then you have to roll your tongue behind very fast. For example in phrases like "el rey", "el río", "el ritmo"... That works to me.
While rhythm and tempo are distinct musical phenomena, in ordinary speech most people use beat, pace, rate, speed, and tempo correctly as synonyms, but often incorrectly include rhythm. Since DL isn't musically sophisticated, I think they should include all those terms as correct translations of ritmo.