Report and parameter caching using portlets

[bdbits]

I have a scenario where the same user logon is used coming in through portlets (SPS). The user can choose from several sets of reports, where each set is linked with drill-down definitions and the top-level report has a prompt page. For instance:
Report 1 -> Report 1A -> Report 1B
Report 2 -> Report 2A -> Report 2B -> Report 2C
Report 3 -> Report 3A -> Report 3B
etc.

The problem is that the single logon, even on different computers is sharing via some mechanism. This includes the report parameters/prompts. With 2 or more real-life-users on different computers, this is a significant problem. For example, opening browsers on two seperate machines might go something like this:

First computer:
  Report 2 (prompted) -> Report 2A -> Report 2B -> Report 2C
  Report 3 (prompted) -> Report 3A and stops
Second computer:
  Report 2, which immediately shows the cached results from first computer's selected parameters
  Reprompts Report 2 via an on-report link and selects different parameters
  Report 2-> Report 2A -> Report 2B works as expected
First computer:
  Goes to Report 2 and sees it unprompted with the second computer's selected parameters

I hope that you can see this is a very undesirable situation. I would be fine with the report rerunning every time, so if I can disable the caching somehow that would be perfect. I tried disabling viewer portlet caching at the server level (per Ch 7 in the admin guide) but that seemed to have no effect. I am not seeing a way to disable user session caches, and am not sure that is even where the problem lies. Is there a way to fix this? I hope maybe I am missing something simple. Code, configuration, any method would be fine.