Publons treats every round of review separately. If you review a manuscript for a second time or third time, we will assign you with a separate review record for each round of reviews performed.
When multiple reviews of one manuscript have been performed by a single author we concatenate them on the detail page (if the paper and review are both published).
To make sure you get separate review records for each round of review, be sure to forward each "Thank you for reviewing' email you receive to firstname.lastname@example.org for each round of review performed.
See this publon as an example: https://publons.com/publon/5158/