With smart phones, you may not be explicitly browsing, but your background services may be connecting to your servers. Think email, it will be checking for new mail periodically. So best to shut off cell service if you think you might have an issue.
I have an old AT&T plan, which evidently does not include CA and Mex roaming anymore. On some recent cruises I had to manipulate things accordingly.
Normally I get a text when it roams, and I quickly shut if off, and haven't been caught out by any charges.
