As you have mentioned that you have created seperate slots and by enrichment you have getting comany, organisation and group. I would suggest you better pass the values Support, Window, Unix as Tier 1, Tier 2 and Tier 3.
So as per your requirement Tier 1 will always be Support and Tier 2 will change (Windows/Unix).
Once you are receiving these values in INT:Staging form your job is done.
Configure assignment with Ope Cat and configure support group accordingly.
Hope this helps...
You need to enrich the events in order to have proper Product and Operational Caterization.
Depending on the values of Product and Operational Caterization the assignment happens on the Remedy side.
You also need to make sure that the Foundation data for the Company being used it configured correctly.
You can achieve this by building a refine and enrich the events $EV.itsm_category; $EV.itsm_type; $EV.itsm_item; values by looking a dynamic data table when events slots like $EV.ev_source, $EV.mc_host, $EV.mc_object_class, $EV.mc_object, $EV.mc_parameter match a particular pattern
This approach will work for BEM but if you have SIM and have CMDB integrated to it and your CI has the attributes of Category, Type & Item added, then you can just use a companent based enrichment policy to attache the same to the event.
Also make sure your IBRSD mapping is enabled to pass these enriched slots to be passed to Remedy.