I am not a Cybran player anymore, but I have been. Now I play Aeon. And I know what it feels like to be playing against a decent Cybran player. Painful. Very painful, at times.
Let's take a map like Open Palms, for instance. I don't like playing Cybran on Open Palms anymore, and here is why. The Mantis are fast. The Mantis have crazy turret capability. The Mantis like eating the Aeon.
Ok, so as we may or may not all know, the Aeon units have a wonderfully long range (at least wonderful from my perspective!). With a land scout parked in the middle of a group of Light Tanks, they can sometimes take out a PD without it firing back a single shot, assuming there are no enemy land scouts or radar near it.
So, what can a Mantis do? Well, get within range, that's what. And by within range, I mean move your group of Mantis IN TO the enemy group. Then start focus firing once you are inside, if you have the time to micro a bit. Heck, it doesn't hurt to even run through them a little.
The firing rate on the Mantis is obscene. A group of 5 of them will definitely wipe out a group of 5 Auroras (or whatever you call the Aeon Light Tank

).
Now, on maps like Open Palms, you can really harass with a few of them. Even the light assault bots as a pair can be painful. They move so quickly, you can easily dance them around and take out a couple Aeon Light Assault Bots and a scout. So, my suggestion as Cybran is to use your units to your advantage, and hit early. Start gaining small resource advantages by slowing your opponent's progression on the map.
Move groups of your units in to attack early before they start getting up PDs or get their ACU in to the mix. In fact, if you can bring your ACU along with a group of Mantis, then start rallying them forward, you could gain a very early game advantage. Then it's just a matter of pushing to keep it. Don't forget to tech! Remember kids, it's all about control. Take the game to them, and show your opponent how you want your game to be!
Good luck.