First i think that Billy showed Tomi loyalty because he was always by his side. Even if he didn not always agree with Tomiś decisions he was still always willing to help him out, because that is what a best freind does. In chapter 2 Billy is asking Tomi if he is sure bringing up Taiyo Maru is a good idea. Tomi seemed to be uncertain but they worked together and tried to do it anyways.
Secondly, i think that Billy showed tomi loyalty by always helping