Under the AOC VBStats hood is a very comprehensive relational database. The database is lightweight so you can store thousands of matches without any problem.
Ideally a player should only have one record in the database. This will ensure consistency and the ability to track the player's performance over the course of their career.
However a new team should be created for each season or even for each tournament. Teams can have the same name but the team codes should include season year or tournament's name so they can be differentiate. For example Falcons 2018 and Falcons 2019. Or AUS VTV14 and AUS VTV15.
When PSVB files are exported, the team and player records are included in the files hence the iPad that imports the files will also inherit these records. If the records already exist then the app will go ahead and use them rather than creating duplications. Now if you create matches on the second iPad using these teams and players and export them back to the first iPad then the we have a situation that multiple iPads sharing a common database which allows cooperative stats sharing.
Here is how a league can organise stats sharing between teams.
By sharing stats like this, teams do not have to spend a lot of time scouting. Instead only the home teams have to code the match for the round whilst every team has access to all the matches played in the round. Another advantage is that the league can generate Best players report for each round accurately and easily.