OK, I finally got it working. This page was invaluable:

http://www.mssqltips.com/sqlservertip/2844/working-with-multiselect-parameters-for-ssrs-reports/

I changed the type of the parameter to text. Then I removed the filter on the detail dataset. Then I added a parameter in the detail dataset's properties. The expression I used is:

=Join(Parameters!pSupervisor_ID.Value,",")

Apparently, the "Join" function is what I needed. Thanks for reading.