Thank you for the post.
To attempt to replicate this I created a new database file with a single global text field, and a text label with the same information. I put the font for both as Helvetica 24, removed field entry for browse mode, and then hosted through FileMaker Server 12's Instant Web Publishing. My fonts display the same in FileMaker Pro 12 and through the browser (see screenshot below).
Perhaps, I am missing a step to replicate?TSFalconFileMaker, Inc.