I made a donation at a shrine which was enough to both give me an emblem and to gain a level. When this happened:
The emblem was deposited in my bag.
I received the popup message in the bottom right corner of the screen telling me I had enough favour for an emblem.
My favour afterwards was zero (ie, I didn't receive the favour for levelling up).
It would appear that the order things processed was:
1. I made the donation.
2. The xp from the donation was applied.
3. I levelled up.
4. I received favour from levelling up.
5. This pushed me over the limit, so I got the message to go to a shrine to collect my icon.
6. The favour part of the donation was applied.
7. Since I was already at max favour, no favour was added.
8. Since I was at max favour after a donation, I received an icon, and my favour was reset to 0.
What I would have liked to happen would be for the favour component of the donation to be applied before the xp part, so I could have got the levelling bonus as well. At the very least, though, this situation shouldn't generate the "visit a shrine to pick up your emblem" message, since that was confusing.
Thanks for your time.