Are you connecting the the Tableau Server directly from an iPad and using active directory authentication? In this case you will always get a login prompt. If you are embedding visualizations in your own web pages then you need to use trusted tickets. See links below:
Sorry, didn't read your question correctly - link may be useful anyway just in case you have not seen it.
I know this thread is bit old, but we were able to finally overcome this issue of 3rd party cookies and get our site where we embedded tableau working on Safari, etc. without the clients having to change any of their default settings by setting up a reverse proxy on our web server using the internal IP of the Tableau Server (same domain).
FYI- For those unfamiliar with what a reverse proxy is, here is a cut and paste definition from wkipedia:
Reverse proxy is a type of proxy server that retrieves resources on behalf of a client from one or more servers. These resources are then returned to the client as though they originated from the server itself - (i.e: no third party cookies)
Generally speaking this is how web load balancer servers work. Pretty easy to setup in either apache or IIS.