Hello @ffremaux, happy to have you in the Community! TSheets is definitely compatible with Quickbooks Enterprise 2019 and should also function as normal in a hosted environment. Depending on the server, you may need to reach out to them directly in order to have them allow/add TSheets, or enable any settings within that environment.
I can provide you with articles on how to integrate your Quickbooks Desktop account with TSheets. There are two ways to connect but since you are in 2019, you should be able to integrate with the windows set up. If for some reason you do not see the option to Activate TSheets, here are the steps to integrate via the web connector.
If you need any help along the way, please feel free to reply back @ffremaux:) We are eager to help you!