Well, I just did some testing, and I can't replicate what you were seeing...
1.) I didn't have any .tmp files on my SSD, so I created one in the root.
2.) I did a backup, and both my primary and secondary backups successfully backed up this .tmp file
3.) I didn't have the exclusion for *.tmp in my exclusions files, so I added it to both my primary and secondary.
4.) Ran another backup, and this time. the .tmp file was not found in the primary or secondary backups
5.) I took a look at the log, and still don't have any tar errors about this.