Import and update rows in Access database based on date changes from Excel

Access syntax is a bit icky but your SET is just setting the update.LastModifiedDate to itself, try the below:

PHP Code: 

UPDATE Incidents INNER JOIN [Update] ON Incidents.[Incident ID*+] = Update.[Incident ID*+] SET [incidents].[Last Modified Date] = [Update].[Last Modified Date]
WHERE (((Incidents.[Incident ID*+])=[Update].[Incident ID*+]) AND (([Update].[Last Modified Date])>([Incidents].[Last Modified Date])));