In my previous team, the reviewer was the main responsible for the code they were approving. They were expected to test locally and should actively hunt for potential issues, such as checking in the logs that the ORM was building correct SQL.
In my current team, the developer is the main responsible for the code they're pushing, and is expected to do all the tests needed. Reviews are more about ensuring code standards, finding possible oversights, requirements mismatches, and so on.
No one strategy is right or wrong, as long as expectations are set and everyone knows their responsibilities and expectations.