After a quick check of the particular puffer (they vary a lot in terms of care and behavior). It'd be best to post down in the marine section, as most of the traffic in this part of the forum is freshwater, and your two species are quite different than the ones many of us are familiar with.
I can't find a species name for the blue stripe, but the valentini puffer will be aggressive towards similar species. If they're in the same genus, it's possible they're stressed from aggression between the two and hiding, but it's also possible this is just normal stress common to new fish (which can be worse in marine tanks, where water chemistry has many more variables). Again, the people in the marine section are far more knowledgeable.
