Having created a Saved View from a view in a design model that has elements in Displayset applied, if this Saved View is attached as a reference into another model all the elements are displayed and the Displayset elements are ignored.
However if the Saved View is applied in the original Model then it displays as expected.
Displaysets are not stored in the file and there can only be one displayset active in the opened file.
A Saved View does have a boolean property called Display Set, which simply means do you want to honor the active Displayset or just show all elements. This property makes sense only when a displayset is active.
Thus Saved View attachments cannot support Displaysets
Since a Saved View does not support the Displayset, an alternative method of limiting the contents in the view must be sort prior to creating the Saved View such as limiting the displayed levels or applying a Display Style with a Display rule if using MicroStation CONNECT Edition or later.
Quickset vs Displayset
Elements are suddenly not visible displayset on / off
Will saved views capture and store display rules