Select one object at a time when using the multiple tag option in order to control the numbering sequence of the tags. The sequence of auto-incrementing is undefined if you use a crossing window or another multiple selection tool.
When you use the same schedule tag tool to tag multiple objects, it ensures that the same property set is attached to each object. When adding schedule tags to objects in an external reference (xref), you can avoid broken links by selecting Attach as the Reference Type instead of Overlay.