The plugin won’t erase or empty the tables if they exist, so it could be there’s an error in the SQL export/import process.
Once you get the tables imported, check that the tables exist and there is data in them (using a tool like phpmyadmin). There are two tables:
Mappress_maps contains the map data. Mappress_posts links the map IDs to post ID.
If the new blog has different post IDs than the old one, you’ll need to edit mappress_posts to link the maps to the correct post(s).