Hi Stuart. Perhaps I can help.
A registration is merely a set of pointers that configures the Genos in a certain way. A registration doesn't contain anything except a set of instructions for the Genos. It has no voices, no styles, no tempos...etc. These are set up for each song you want to play. You can play any song without setting up a registration, but doing so means you would need to set the Genos up for the same song starting from the beginning each time. A registration saves a ton of time. You can even have 10 different setups for the same song within one registration, hence, the ten buttons.
For example, when you save a Registration for the song, "Mary Had A Little Lamb," you would have selected items in the Registration Memory window such as: Voice, Multipad, Transpose, Foot Pedals, Style, and other parameters in the list. When you want to play a song that needs the Mambo 5 style, the style must either reside in the Genos list of styles or be imported to the User area via USB drive or stored on the Internal drive of the Genos. As Fred mentioned, it sounds like the Mambo 5 style has not been brought over from the Tyros 5. The Genos can't find it. To the Genos, it simply isn't there.
Here's an analogy. You go on a trip and check into a hotel (Genos). You want to wear your blue socks to dinner, but you left them at home (Tyros). You will have to wear different socks to dinner. To extend the analogy, you would grab the next best sock color - say brown. The Genos does the same thing. It sticks another style in when it can't find the Mambo 5 style. The same idea applies when there was a custom voice made on the Tyros 5 for that song. It too must be brought across and stored on the Genos. Hope this helps.