It sounds like the WebI report has "Refresh on Open" enabled so that when you view, you're receiving the prompts and the query is running automatically. There may be an issue with that. Can you try disabling the refresh on open and see then if the initial refresh works as expected?
Additionally, is there anything special about the Universes or prompts?
For example, are any of the prompts cascading LOVs? Do the Universes have any access restrictions/overloads on them?
I have seen this issue in XI 3.1 with nested LOVs, but was corrected prior to BI 4.0 being released, so likely not the same issue.
Regardless, it does sound as though it may be a defective behavior, just looking to narrow potential cause to see if it matches anything that might already be reported (so Simone's tracing recommendation would definitely be a bonus!).
Carly