It should have automatically converted to the new theme but it's not. How do I make it so the plugin codes such as NewPoints show up in a new theme?
Because they shouldn't automatically be converted...the template edits are typically run in the install or activate functions. So basically deactivate and reactivate the plugin.
Would that not get rid of plugin settings though?
No it shouldn't, uninstalling deletes settings/tables/etc.
It varies plugin to plugin, but typically deactivating wouldn't, and shouldn't, delete settings.