To go ballistic means to become wildly or uncontrollably angry, so the motivation in this sentence is for him to stay calm should he be likely to get extremely angry.
Consider the statement "Just in case I needed some motivation for him to stay calm should he be likely to get extremely angry at me.". Is the statement "Just in case I needed some motivation for him to calm down should he be inclined to go ballistic on me." false? Yes/no/unknown