Database placement on abstract storage structure
What I would do is to benchmark the performance before and after the changes. There should be a performance gain after tempdb is moved to another drive. Use DMVs like sys.dm_io_virtual_file_stats to see the read and write wait times for the DB files. 

Use the perfmon physical disk counters: Avg. Disk sec/Read, Avg. Disk sec/Write, Disk Reads/sec, Disk Writes/sec. The change in these metrics will let you know if the disks are physically separate or are just the same disks which are logically separated.

Want a third party disk benchmarking tool for your disks, so that the SAN admins cannot accuse SQL server of its results? Use SQLIO. Although there is SQL in the name, this tool does not require SQL server to run and is not related to SQL server.

This is a good question, and I look forward to see the other answers.