You are going to have more issues than just search and search pagination if Premise is only detecting by forum category and/or post_parent in wp_postmeta.
I expect you will also find them turn up via widgets, shortcodes and custom registered views.
If Premise was detecting by each off bbPress’ post types, forum, topic and reply specifically rather than forum category alone you would find that it would also filter these results correctly from search also alleviating your pagination issue whilst also making sure they didn’t turn up in via widgets, shortcodes or custom views.
