I don't know how their cohorts work but in Repeat Customer Insights the cohorts use the order's adjusted values as described in the previous article (i.e. refunds adjust the original order's amount).
That means a refund has only two places it impacts cohorts:
- The Totals for the original cohort are adjusted down
- The specific month of the original cohort are adjusted down
Say for example an order is refunding in 2023-03 for an order placed in 2023-01 for a customer who first ordered in 2022-05.
- The totals for their 2022-05 cohort would be adjusted down
- The 2023-01 month in that cohort would be adjusted down (the 8th month)
- Nothing would happen to the 2023-03 cohort
That's the correct way a cohort report should handle refunds: by adjusting the original cohort.
Cohort reports are 100% behavior reports so I'd hope there's no skewing involved on Shopify's side.