We've experimented in the past with both models - new fields appear automatically, and reports are frozen. Both had their set-backs. When Omniscope became fully "tab-ified", there's no clear distinction between a "report" and a tab. You're always in a tab, but might be using it just as a workspace. So we settled on new fields appearing automatically.
You can "freeze" a tab's visible fields quite easily: Settings > Advanced tab settings > Freeze visible fields. This will prevent changes *in other tabs* (or automatic, such as on refresh data) from causing fields to appear in the current tab.
(But if you explicitly choose to add a field, it will still appear by default in the current tab, regardless of this setting).