Execution time of a stored procedure
This happens because SET STATISTICS TIME ON will give you summarized time results for a stored procedure in addition to time results for each query that's part of the stored procedure. Let's run a simple test to try to reproduce what you saw. The following code isn't important except that it runs for a few seconds on my machine:

set statistics time on;

WITH E00(N) AS (SELECT 1 UNION ALL SELECT 1),
        E02(N) AS (SELECT 1 FROM E00 a, E00 b),
        E04(N) AS (SELECT 1 FROM E02 a, E02 b),
        E08(N) AS (SELECT 1 FROM E04 a, E04 b),
        E16(N) AS (SELECT 1 FROM E08 a, E08 b),
        E32(N) AS (SELECT 1 FROM E16 a, E16 b),
   cteTally(N) AS (SELECT ROW_NUMBER() OVER (ORDER BY N) FROM E32)
SELECT AVG(CAST(N AS BIGINT)) 
FROM cteTally
WHERE N &lt;= 10000000;

WITH E00(N) AS (SELECT 1 UNION ALL SELECT 1),
        E02(N) AS (SELECT 1 FROM E00 a, E00 b),
        E04(N) AS (SELECT 1 FROM E02 a, E02 b),
        E08(N) AS (SELECT 1 FROM E04 a, E04 b),
        E16(N) AS (SELECT 1 FROM E08 a, E08 b),
        E32(N) AS (SELECT 1 FROM E16 a, E16 b),
   cteTally(N) AS (SELECT ROW_NUMBER() OVER (ORDER BY N) FROM E32)
SELECT AVG(CAST(N AS BIGINT)) 
FROM cteTally
WHERE N &lt;= 1000000;


Abbreviated output from SET STATISTICS TIME ON:


  SQL Server Execution Times:    CPU time = 3407 ms,  elapsed time =
  3450 ms.
  
  SQL Server Execution Times:    CPU time = 343 ms,  elapsed time = 388
  ms.


As expected, there are two separate measurements for the execution time with the second query running in about one tenth of the time of the first. Now I'll create and run a stored procedure that just calls the above code. Abbreviated output from SET STATISTICS TIME ON:


  SQL Server Execution Times:    CPU time = 1187 ms,  elapsed time =
  1201 ms.
  
  SQL Server Execution Times:    CPU time = 110 ms,  elapsed time = 117
  ms.
  
  SQL Server Execution Times:    CPU time = 1297 ms,  elapsed time =
  1319 ms.


The math works out for my simple example: 1187 + 110 = 1297 CPU time and 1201 + 117 = 1319 elapsed time.