Current transaction isolation levels do not prevent others from reading and modifying the same data.
They all wait nice in line to be able to update the same rows, but there is no way of preventing them from overwriting the previous data, and no error message that the data you selected has become stale in between.

An easy way to solve it to allow a way to lock the selected rows to assure that the current transaction is finished before the next one can read the value and do its own changes.

This is easely done by just adding a small statement to the select SQL:

MySQL,PosgreSQL,Oracle: "FOR UPDATE" at the end
SQL Server: "WITH (updlock)" before WHERE