Just learned this from personal experience.  Hoping to save someone else some pain.

I tried the following searches:

mysql transaction partial rollback
does fetching commit an innodb transaction
innodb rollback not working

The symptoms I was experiencing included inserted records were rolled back, but an update to a table was not. My PHP code threw an exception inside a transaction, and the catch did a rollback, but the update still went through.

The problem was that the table I was updating happened to be MyISAM. MySQL silently ignored the fact that I included a table in my transaction that couldn’t be rolled back. When the rollback occurred, this was also silently ignored.

Moral of the story: use all InnoDB if you’re going to be doing transactions.