Hey @dannilundgren ...when we were moving to Jamf Connect with Azure, I watched this video and it helped immensely....

https://trainingcatalog.jamf.com/path/get-started-with-jamf-connect/configure-jamf-connect-for-azure-ad/614284

Also, here is a link to the Jamf documentation on setting up Jamf Connect with Azure.  

Integrating_with_Microsoft_Azure_AD.html

Hope it helps.  

Regarding this comment: "When I open Authenticator after enrollment, nothing seems different; I still have to sign in, as if I used it on my private device."
There are specific Azure settings as well as policies that do need to be set up to send an MFA prompt or for you or your end users to get a visual on how all is working or not working. 

If you have not configured both sides of the process then yes the link and info @steve_summers  posted will be helpful.

Thank you for your responce. - I have forgotten to point out that this is regarding Jamf School and Azure SSO on iPads. We do not have Jamf Connect. We have only configure the Single Sign-on payload in a profile in Jamf School.

I am 100% on the Jamf School and SSO integrations but I would think it is still true you need to have the enterprise app and app registration done so the handshake (for lack of a better word) takes place and end-used can authenticate properly and security.  This is the Nation I am certain others will chime in when they have a second. Hang in there!