Books Online has some nice scriptlets for monitoring the tempdb version store : "Troubleshooting Insufficient Disk Space in tempdb ".
To get a hunch, perhaps you can trace some representative workload and re-run it on a test server using the SNAPSHOT isolation level (and monitor with some of the scriptlets from BoL for instance)?
You will notice that the version store is used for many things - even when SNAPSHOT isolation level is not turned ON (such as temporary work objects used during query execution and triggers). E.g., this simple query in Adventureworks will use 8 pages in the version store in READ COMMITTED:
UPDATE Sales.SalesPerson SET SalesYTD = SalesYTD + SubTotal FROM Sales.SalesPerson AS sp JOIN Sales.SalesOrderHeader AS so ON sp.SalesPersonID = so.SalesPersonID AND so.OrderDate = (SELECT MAX(OrderDate) FROM Sales.SalesOrderHeader WHERE SalesPersonID = sp.SalesPersonID)
The following query:
SELECT SUM(version_store_reserved_page_count) AS [version store pages used], (SUM(version_store_reserved_page_count)*1.0/128) AS [version store space in MB] FROM sys.dm_db_file_space_usage