Look at Settings - iTunes & App Store. The Apple ID will be visible there. If it's his, this is the reason for purchases appearing on his new iPad Air 2. If it's yours: do you use Family Sharing?
I'm wondering which backup he used when he set up his device. Safari bookmarks only appear on both devices when they are both set up with the same iCloud ID. As you both use different ones, this should not happen. Did he use your iCloud ID when he set up his device? This would explain both: your purchases and bookmarks appearing on his iPad.