Tagging across external references works best when using the Drawing Management features of ADT/ACA (Project Browser/Project Navigator). In that environment, ADT/ACA "knows" that the data should live at the Construct level (not at the Element or View levels) and property data overrides will be attached to external references as needed to achieve that (none in the View file; on Elements in the Construct file).
Outside of the Drawing Management environment, ADT/ACA has no way of "knowing" where an override should or should not be placed, and so it always places an override in a file when tagging an externally dependent item. You have to be aware of that and manually remove the override in places where you do not want it. In the early releases that supported tagging through external references, the process was tedious and the results, even after the override was removed, were unacceptable (tags would not update when base drawing data was changed). My firm is still largely using 2004 (2008 is promissed "soon"), so we tag doors and spaces in the "base" drawing, to avoid update issues.
One item that we have had success tagging through external references is partitions, where, like you, we have a style-based property that holds the partition "ID" string. Unlike you, we do not have a provision for overriding the tag value - we would simply copy the style under a new name and edit the partition type "ID" string in the copy, if we had a partition of similar construction that needed to have a different partition type called out in the tag
I had never tried to set up an object-based PSD that tried to override a style-based value -AND- then tried to apply the override through an xref. As your sample files demonstrate, that does not appear to work. The object-based PSD in the base file correctly shows the style-based value when no override is present, but when used as an override when tagging through an xref, it fails - most likely because the style-based property set does not get placed as an override, so there is no WallStyles:Type property associated with that wall in the host file to have a value to report.
Removing the override in the host file allows the tag to read the value from the correctly functioning formula in the object-based Wall property attached to the wall in the base drawing, so it would appear that you will want to do that if you are going to need to have the tags in the host file, and not in the base file. You can do that after the fact, or at the time of tagging in the host file, by remembering to set the appropriate data source in the Edit Property Set Data dialog when tagging or in the Edit Referenced Property Set Data dialog when editing after the fact.
--
David Koch
Autodesk Discussion Group Facilitator
Using ADT 2004 at work; access to 2005, 2006 & 2007 at home