I believe that they don't show up until the game announces with a popup window that you're getting them. It's not my understanding that they start up unannounced.
That should be the case. IME, you'll get this popup when you log in if they've activated:
https://forum.us.forgeofempires.com/index.php?attachments/6364/
There should be a single incident in your city to find. You'll get a second popup once you click on it. After that, the incidents should start appearing randomly. I find it's best to just do a city sweep for them when you first log in, they're supposed to last 24 hours. I was getting 2-5 on my first log in during the testing period, and occasionally 1 or 2 after logging in later in the day. Inno's wiki states 10-15 a day though, and I had bout 9 this morning. Possibly the full rollout changed the number available.
Hmmm...I'll wait till the 19th before jumping on my soap box...from what my guildies tell me, incidents are not that crucial to competitive gameplay. More like a little gift for searching the grounds....
They're not. The supplies and coins are about what one would get from the first part of the treasure hunt. However, you'll only find coins and supplies with the common encounters, unlike how the lowest levels of the treasure hunt only has coins and supplies. There's fps and medals on all levels of incidents, fps are 2, 5, and 10 respectively. The uncommon and rare incidents can give out small amounts of goods. There's bp as well from the better incidents. Uncommon incidents can have motivation kits, and rares can have small boosts or 5 diamonds.
Compared to treasure hunt, there's more varieity with the rewards. Treasure Hunt does increase coins and supplies with every step on the hunt, while with incidents the amount remains piddling. However, there's a chance for coins and supplies every step on the Treasure Hunt, while incidents keep them confined to the common ones, though most of your incidents will be common.