Hi Martey,
This won't be what you wanted to hear, but it's actually the log messages which are a red herring. UD is meant to back up only the WordPress tables... there is a slight difference in what's logged; here's a WP table:
0051.836 (0) Table wp_terms: Total expected rows (approximate): 8
0051.848 (0) Table wp_terms: Total rows added: 8 in 0.01 seconds
0051.850 (0) Table wp_terms: finishing file (backup_2013-11-04-2202_Council_on_Education_for_Public__(redacted)-db-table-wp_terms.table.gz)
Whereas the one not being backed up only gets this:
0051.855 (0) Table program: finishing file (backup_2013-11-04-2202_Council_on_Education_for_Public__fe9e1a6c072b-db-table-program.table.gz)
If you look in the actual database backup file itself, then there should be a message that says that the non-WP table was skipped.
I've changed that now, so that in the next release the log will explicitly indicate that the non-WP table wasn't backed up.
However, having said that... the ability to add other, non-WP tables has been a feature that's been requested, and we plan to add it to UpdraftPlus Premium. Presently, we've got working code that can do this in a very simple way - it can do what you want (i.e. add all tables found in the MySQL database). If you buy UpdraftPlus Premium and then give me a shout, then I can email the new version over to you.
Best wishes,
David