Thank you for taking the time to reach out to us here on the Community page. I'm here to help check why your May statement is coming up with June statement.
First, please ensure to only select the month of June when downloading the statement. It's possible that the month of May was included. If you're using QuickBooks Online (QBO) and if you've selected the correct month yet the statement for the month of May is still coming up, you may need to try clearing the cache of the browser's you're using to check if the issue is browser related.