Hello,
Not sure i see an issue here. The AI is considering your puppet as an enemy, because it is at war with you and you could at any point call it in and have it become hostile to them. The AI leaving such borders unguarded would make it very exploitable. It looks like it is outnumbering you about 3:2, which seems like an okay ratio. If it was heavily overcommitting to the border there could be a problem, but this seems to be it just avoiding leaving borders to (potential) hostiles open, it has a very good reason to guard borders to puppets of countries it is at war with.
Not sure i see an issue here. The AI is considering your puppet as an enemy, because it is at war with you and you could at any point call it in and have it become hostile to them. The AI leaving such borders unguarded would make it very exploitable. It looks like it is outnumbering you about 3:2, which seems like an okay ratio. If it was heavily overcommitting to the border there could be a problem, but this seems to be it just avoiding leaving borders to (potential) hostiles open, it has a very good reason to guard borders to puppets of countries it is at war with.