pg_search gem and fulltext search rank setting
I had a very similar situation in Django and I solved summing up the trigram similarity and tsearch rank.
Similarity with word with exact match is higher than a partial match, as you can check on PostgresSQL:
SELECT similarity('gro', 'gro') AS exact, similarity('gro', 'group') AS partial; exact | partial -------+---------- 1 | 0.428571I'm not a ruby expert but I've read the pg_search documentation and I think the solution for your question should by similar to this:
pg_search_scope :fulltext, against: [:firstname, :lastname, :middlename], using: { tsearch: { prefix: true }, trigram: { :threshold => 0.2 } }, :ranked_by => ":tsearch + :trigram"