On Publons, each round of peer review of a single manuscript is considered separately. If you review a manuscript for a second or third time, we will assign you with a separate review record for each.
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). See this paper as an example: https://publons.com/publon/5158/
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 email@example.com for each round of review performed.