Turns out that we should probably pass the ObjectType when marking the temp object. Build is fixed (temporarily).

Author: lizbaron

Source/tSQLt.FakeTable.ssp.sql

@@ -49,7 +49,7 @@ BEGIN
 
    EXEC tSQLt.Private_CreateFakeOfTable @OrigObjectCleanQuotedSchemaName, @OrigObjectCleanQuotedName, @TargetObjectFullName, @Identity, @ComputedColumns, @Defaults;
 
-   EXEC tSQLt.Private_MarktSQLtTempObject @OrigObjectFullName, @OrigObjectNewName;
+   EXEC tSQLt.Private_MarktSQLtTempObject @OrigObjectFullName, N'TABLE', @OrigObjectNewName;
 END
 ---Build-
 GO

Source/tSQLt.Private_MarktSQLtTempObject.ssp.sql

@@ -3,7 +3,7 @@ GO
 ---Build+
 CREATE PROCEDURE tSQLt.Private_MarktSQLtTempObject
   @ObjectName NVARCHAR(MAX),
-  --@ObjectType NVARCHAR(MAX),
+  @ObjectType NVARCHAR(MAX),
   --@ParentObjectName NVARCHAR(MAX) = NULL,
   --@ParentObjectType NVARCHAR(MAX) = NULL,
   @NewNameOfOriginalObject NVARCHAR(4000)
@@ -17,17 +17,21 @@ BEGIN
      FROM sys.objects O 
     WHERE O.object_id = OBJECT_ID(@ObjectName);
 
+   --SELECT 
+   --@UnquotedSchemaName,
+   --@UnquotedObjectName;
+
    EXEC sys.sp_addextendedproperty 
       @name = N'tSQLt.IsTempObject',
       @value = 1, 
       @level0type = N'SCHEMA', @level0name = @UnquotedSchemaName, 
-      @level1type = N'TABLE',  @level1name = @UnquotedObjectName;   
+      @level1type = @ObjectType,  @level1name = @UnquotedObjectName;   
 
    EXEC sys.sp_addextendedproperty 
       @name = N'tSQLt.Private_TestDouble_OrgObjectName', 
       @value = @NewNameOfOriginalObject, 
       @level0type = N'SCHEMA', @level0name = @UnquotedSchemaName, 
-      @level1type = N'TABLE',  @level1name = @UnquotedObjectName;
+      @level1type = @ObjectType,  @level1name = @UnquotedObjectName;
 END;
 ---Build-
 GO

Source/tSQLt.SpyProcedure.ssp.sql

@@ -33,7 +33,7 @@ BEGIN
 
     EXEC(@CreateProcedureStatement);
 
-    EXEC tSQLt.Private_MarktSQLtTempObject @ProcedureName, 'PROCEDURE', @NewNameOfOriginalObject;
+    EXEC tSQLt.Private_MarktSQLtTempObject @ProcedureName, N'PROCEDURE', @NewNameOfOriginalObject;
 
     RETURN 0;
 END;

Tests/FakeTableTests.class.sql

@@ -1103,7 +1103,7 @@ BEGIN
   CREATE TABLE FakeTableTests.TempTable1(i INT NOT NULL);
   CREATE SYNONYM FakeTableTests.TempSyn1 FOR FakeTableTests.TempTable1;
 
-  DECLARE @OriginalObjectId INT = OBJECT_ID('FakeTableTests.TempTable1');
+  DECLARE @OriginalObjectId INT = OBJECT_ID('FakeTableTests.TempSyn1');
 
   EXEC tSQLt.FakeTable 'FakeTableTests.TempSyn1';