How to call Data Adapter in a Business Rule?

You could use the FDX queries to extract the Cube View data directly into a DataTable, then iterate through the rows and replacing time names with sortable names, e.g. 2022M5 --> 2022M05.
The FDX would not require a separate Data Adapter to retrieve the cube view information.

Here is a sample on how to fake the period names so the BI Viewer components will sort them in the correct order (rename the .txt to .xml before importing)

To call this from a Data Adapter, here is a sample query:
{SortCubeViewTest}{GetCubeViewData}{CubeViewName=[PPE],|!WfProfile_Assigned_Entities!|}

Snippet

Case Is = DashboardDataSetFunctionType.GetDataSetNames
    Dim names As New List(Of String)()
    names.Add("CubeViewTest")
    Return names

Case Is = DashboardDataSetFunctionType.GetDataSet
    '-- {SortCubeViewTest}{GetCubeViewData}{CubeViewName=[cube view name]}
    If args.DataSetName.XFEqualsIgnoreCase("GetCubeViewData") Then

        Dim strCVName As String = args.NameValuePairs("CubeViewName")
        Dim nvbParams As New NameValueFormatBuilder(String.Empty, args.CustomSubstVars, False)

        Dim dtResults As DataTable = brapi.Import.Data.FdxExecuteCubeView(si, strCVName,
                                                                            "HoustonEntities", "E#Houston",
                                                                            "Scenarios", "S#Actual",
                                                                            "T#2018M1", nvbParams, False,
                                                                            True, String.Empty, 2, False)
        If Not (dtResults Is Nothing) Then
            For Each dr In dtResults.Rows
                Dim strTime As String = dr("Time").ToString()
                If strTime.Length = 6 AndAlso strTime(4) = "M"c Then
                    strTime = strTime.Substring(0, 5) & "0" & strTime.Substring(5, 1)
                    dr("Time") = strTime
                End If
            Next
        End If
        Return dtResults

    End If
End Select

Result: notice the Time column is now been 'faked' into a sortable name.
If you want to make it like "Jan","Feb","Mar" then the BI Anaytics components will probably sort it alphabetically and mess up the order again.  You would need to show both columns, one to force the sort order, and another for the descriptive part.