Row count < 1 Return 0

I'm not 100% sure what you are after here, so bear with me. Your subselect (X) is only going to return one run, by rights, because you are calling GROUP BY on the same fields as your WHERE (and that WHERE is a pure = filter).

Do you want everything other than the job, year and period you select to become 0 in your table? If so, for readability, try doing it in two queries:

UPDATE @Totaltbl SET  
    TTLPerRevAj = 0,
    TTLYTDRevAj = 0, 
    TTLJTDRevAj = 0

UPDATE @Totaltbl SET  
    TTLPerRevAj = X.TTLPerRevAj, 
    TTLYTDRevAj = X.TTLYTDRevAj, 
    TTLJTDRevAj = X.TTLJTDRevAj
FROM ( 
    Select 
        SUM(Table2.Col1) TTLPerRevAj, 
        SUM(Table2.Col2) TTLYTDRevAj, 
        SUM(Table2.Col3) TTLJTDRevAj 
    FROM dbo.Table2
    Where (Table2.Job_Number = @Job_Number) 
        and (Table2.Period_Year = @Period_Year) 
        and (Table2.Period_Number = @Period_Number)
    Group By Table2.Job_Number, Table2.Period_Year, Table2.Period_Number
) X

If you really want to do it in one query, try:

UPDATE @Totaltbl SET  
    TTLPerRevAj = X.TTLPerRevAj , 
    TTLYTDRevAj = X.TTLYTDRevAj, 
    TTLJTDRevAj = X.TTLJTDRevAj
FROM ( 
    SELECT
        TTLPerRevAj = SUM(CASE WHEN t2.Job_Number = @Job_Number 
                               AND t2.Period_Year = @Period_Year
                               AND t2.Period_Number = @Period_Number
                          THEN t2.Col1
                          ELSE 0
                          END), 
        TTLYTDRevAj = SUM(CASE WHEN t2.Job_Number = @Job_Number 
                               AND t2.Period_Year = @Period_Year
                               AND t2.Period_Number = @Period_Number
                          THEN t2.Col2
                          ELSE 0
                          END), 
        TTLJTDRevAj = SUM(CASE WHEN t2.Job_Number = @Job_Number 
                               AND t2.Period_Year = @Period_Year
                               AND t2.Period_Number = @Period_Number
                          THEN t2.Col3
                          ELSE 0
                          END) 
    FROM dbo.Table2 t2
    GROUP BY t2.Job_Number, t2.Period_Year, t2.Period_Number
) X

(but I bet there are better ways.)

Otherwise, you need to be a bit more specific about what it is you are really trying to do?