I would say this means your SharePoint Visio Services are not configured properly.
Most probably it is a security issue (account under which SharePoint VisioServices serviced application runs is not allowed to access your data list, or secure store is not configured)
If you have admin access to the SharePoint, you should login to the SharePoint as admin and configure your VisioServices properly (see the links below).
If you don't have access you could ask your admin/support to do that for you.
There is nothing you can do in Visio to resolve that.
About the refresh time - if you want an instant refresh, you could disable caching (set it it zero), again in the SharePoint VisioServices settings.
Microsoft has has written a lab guide how to configure things in SharePoint, "Configure Visio Services"
https://technet.microsoft.com/en-us/library/jj900483.aspxYou may be especially interested in "Configure Visio Services data refresh using an external connection":
https://technet.microsoft.com/en-us/library/jj900487.aspx