I have finished campaign, but i never got a message that quests are available. I learn from forum, and i started to do quests (i did couple of them, 5-6). I had like 2 weeks break and when i logged i got this message that now i can do them.
Yeah, I think they made some changes to the early quests unlocking earlier - not 100% sure, but there was some talk about it in the build notes recently. I believe you get this prompt later due to having already passed that stage where it would come up originally. Likely not an issue for new players.
The point is i have finished campaign, by which i mean i did CardStock II Secret Preview. After that no new missions were available, and yet, i did not get the message about quests.