Does the statute of limitations apply to an amended complaint that adds a new defendant?

"The general rule is that an amended complaint that adds a new defendant does not relate back to the date of the filing of the original complaint and the statute of limitations is applied as of the date the amended complaint is filed, not the date the original complaint is filed. [Citations.] A recognized exception to the general rule is the substitution under [Code of Civil Procedure] section 474 of a new defendant for a fictitious Doe defendant named in the original complaint as to whom a cause of action was stated in the original complaint." (Woo v. Superior Court (1999) 75 Cal.App.4th 169, 176 (Woo).)