I was shocked. He had his there, (the other was at a faraway planet) and was constructing three more. I smashed them all.
As it turns out, their Vasari Player had constructued two Kosturas in the confsuing and blew us to bits.
To be honest, all of you lost the moment you allowed them to build so many super weapons. That said, the TEC player could have delayed their deployment or destroyed them with a rush of spammed scouts with their anti-building ability researched.
To build two novas at the same time meant that he did not have enough resources for a fleet, which also meant that you didnt attack him earlier, or else you would have witnessed his few forces and continue on to conquer him earlier.
Me and my Advent ally rush to get a Kostura. Once I get it, I fired at Peleneos, figuring it would damage the nearby Nova (First time I built the Kostura) (And I managed to see the Nova right next to the planet)
Total failure, while I hope it serves you as a hard learned lesson. You should have known that your super weapon would not destroy his weapon. Second, you did it wrong, you REACTED to them building super weapon with you building super weapons, that was stupid, there was no way you could win, they already had a headstart. What you must do in that situation is exploit their weakness, that is, their small fleets. Attack them head with all your ships, dont waste resources in a super weapon (unless you have ample or already have max ship cap) and build ships to destroy his planets.
By now I'm pissed off. I declare ultimate war on him (Three star systems) and invade his system with two Kortuls, two Skirantas and a Space Egg. I smash his defenses by surprise. I quickly colonize and fortify that planet with 5 Missile Platforms and 2 hangars. I continue until I get to Peleneos.
That finally sealed your team fate. You lost time colonizing and fortifying and insignificant planet, one which would not be subject to counter attack, you should have pressed on to the planets with the weapons.
Your team got owned hard, but remember, the best defence is a good offense. Dont let it happen twice. 
Would that be considered spamming? He fired at least twenty rounds all in all from his Novas- and kept hitting my planets.
No, that would be considered good use of his Novas, or, as i would put it, Victory.