It should all work the same, but you might to provide some more details. Which version of MySQL are you using? Is it running on the Mac or another box? Which JSP container are you running? Do you have the MySQL drivers in the right place? Are you getting any error messages? etc, etc. Hopefully somebody will be able to help you out if you give them some more info.
Yup, we'll need more details. JDBC per se has no cross-platform issues that I am aware of. I have web apps running on Windows, Mac OS X, and Linux that all connect, using the exact same JDBC code, to a PostgreSQL database running on Solaris.