Currently, my PhD is devoted to answering this question. It is tough question to answer as there is very little public pronouncements explaining the reasons for their support. It is a bit of a mystery really as this region is uniquely vulnerable to the court's prosecution. I have identified the following possibilities based on theories highlighted by the international criminal justice literature and explanations that I have inferred from the facts I've accumulated.
(1) States were persuaded to commit to the ICC after sustained exposure to a campaign organized by global civil society and like-minded states. In the simplest terms, angelic "states" like Canada and EU member states and NGOs like Amnesty International put forward a compelling argument: "civilized states support ending impunity for egregious human rights violations. Are you a civilized state or a pariah state?"
(2) This is somewhat related to the previous explanation. African states that have been democratizing over the last two decades have witnessed the opening of new political channels to pressure their governments. These channels were utilized by a highly committed civil society campaign. The governments in turn responded by supporting the ICC.
(3) African states supported the ICC in response to pressure from key donors like the EU. This would appear to be the most obvious explanation. These states were (still are) highly reliant on donors to pay for the functioning of their country (or simply to maintain their patronage network). For the EU, the ICC represents an important means of asserting their normative identity on the world stage.
(4) States which lack the means to quell rebel threats in areas free from governmental control saw commitment to the ICC as an opportunity to not only assist the government in arresting these rebels but also in delegitimizing their cause. We are talking about states like the DRC, Uganda and CAR.
(5) Somewhat related to the above explanation but whose instrumental use of the ICC is quite different. Governments which have been afflicted by conflict committed to the ICC to signal to their domestic opponents that they were committed to peace and no longer sought to use excessive force.
These I feel are the most plausible and the explanations which I am currently testing. The results should provide a key insight into one most puzzling political phenomena over the last few decades: the region's initial embrace of an institution calibrated to reduce the government's discretion over national security as well as prosecute any individual seen have got on the wrong side of the "international community".