Tags are supported using the default configuration. This assumes Branch to Build filter is set to an empty value. If you do not want tags to be processed, they can be disabled from either the Bitbucket or Jenkins side.
Pipeline jobs support tags. It requires setting Branches to Build parameter to **/**.
Multibranch pipeline with Git plugin
As of September, 2018 it's not supported. Git plugin represents tag as branch and then it gets filtered out
Multibranch pipeline with Bitbucket Branch Source plugin
As of September 2018 multibranch pipeline with Bitbucket Branch Source plugin is not supported. This is similar to the Git plugin issue:
Additional details can be found here: