From what I understand, the refugees are primarily in Rwanda, and there are some in Tanzania. Both countries have a long history of providing protection to refugees. However, we understand that because there have been some words shared between the governments of Burundi and Rwanda, there is a different dialectic at this time from Rwanda. That being said, again, when refugees cross a border, it is the UN High Commissioner for Refugees who provides protection and assistance.
Tanzania has an incredibly long history of hosting those seeking asylum.