The relationship between Arcobaleno and Vongola started with Reborn And The 9th Vongola Boss. The First Meeting of all seven Arcobaleno and 10th generation family was in the present. The 10th family need to collect all seven of the Arcobaleno seals to open their Vongola Boxes.
The Arcobaleno became their tutors to get the 1st Gen Family's inheritance (Primo's Family). Because of that, the Arcobaleno learned many things about Tsuna's Family.
In the manga, Tsuna's Family scattered to different teams of Arcobaleno to became their Representatives.
Also, both groups hold parts of the Tri-Ni-Set.