Something like that??
CREATE TRIGGER tr_Employee_Insert
ON dbo.Employee
FOR INSERT 
AS
    UPDATE b
    SET Status = 'Inserted'
    FROM dbo.Employee_Backup b
    INNER JOIN Inserted i ON b.EmployeeID = i.EmployeeID
CREATE TRIGGER tr_Employee_Update
ON dbo.Employee
FOR UPDATE
AS
    UPDATE b
    SET Status = 'Updated'
    FROM dbo.Employee_Backup b
    INNER JOIN Inserted i ON b.EmployeeID = i.EmployeeID
You basically need to join the Inserted pseudo table which contains all rows that have been inserted (or updated) from the base table (dbo.Employee) and the Employee_Backup table - and then use that result set from the JOIN as the basis for your UPDATE statement.
Note: this will NOT insert any new rows into Employee_Backup when you add new rows to dbo.Employee - is that what you want? If not, you'd have to change the FOR INSERT trigger a bit ....