When young Joe unwraps his rifle, the bolt handle is on the left side of the weapon. Bolt-action rifles have their handles on the right side, so the picture is flipped.
When Joey unwraps his .22 rifle it is a left handed model, meaning the bolt is on the left side, some bolt actions are made specifically for left handed shooters, not all are right handed. The gun being a right handed model later on is a continuity error, not a image flip mistake.