Ah! I figured it out!
I'm playing with my friend on the LAN. Neither of us were getting spells, but I ran into another bug and tried to relog to solve it. When I relogged into the server (hosted by my friend), all my spells showed up! My friend, the host, also had to relog into his server for him to get his rewards, so something's not quite right in MP at the moment.
The second bug I ran into was I had 8/10 upgrade slots used (+5 mana and +3 attack from the tutorial). I went to the settlement merchant and bought a +2 health stone. For the life of me I could not equip it, either by right-clicking or dragging. That's why I relogged to the server, I was then able to equip it, and I noticed all my mission rewards showed up as well (not sure if that was related).
Hope that helps!