I've been working with the VPP part this morning. When I assign a managed app to me I'm not getting any kind of notification on either of my devices to install the application. On VPP Invitations tab I have Method set to "prompt users on their mobile devices" selected. But I do not get a prompt on either device. If I go into the App Store it shows the app under purchased with the down-load cloud next to it, and i can download it. When I pull the application from me it will disappear and no longer be in the App Store under purchased.
Are you trying to use the VPP portion with the "managed licenses" or just push out apps in general? It sounds like the first option. If that's the case, when I went to VPP invitations, under scope I chose the user and sent out the invite. I did see an invite pop up on the screen, but I don't recall if it popped up in general, or if I had to go into self-service or the app store for it to appear; I did however see the invite. The other thing you can try if the invite doesn't come through is to go to the iPad profile in JSS and do an "update inventory" and then "blank push." Also try rebooting.
Once the invite went through, I went to VPP assignments, added the app I wanted to distribute, went to OPTIONS >> APPS and chose the app I wanted, chose the scope accordingly and clicked on DONE. The app however didn't appear in self-service, but it does appear in the app store under "purchased" and you just download it there. I've read stuff about a "silent install," but have yet to see anything like that happen yet.
The other piece to know is that I did have to download a token for the app that had managed licenses which I then uploaded to JSS. To get the token, I had to log in to apple's VPP site, click on the dropdown in the upper right and choose "account summary." From there I saw an option to download a token. To upload it, when in JSS, you have to be in MOBILE DEVICES, choose "management settings" from the left menu pane, go to GLOBAL MANAGEMENT, and then create the new VPP profile there and upload the token accordingly.
I hope some of this proves helpful for you.