Read the passage again, it's obvious that Cyndane isn't even sure if Alivia can channel at all until she actually embraces saidar. And doesn't note Alivia's strength until she has weaves to defend against. The vast strength being thrown at her is why she instantly knows Alivia has an angreal as well... from what we've seen of that particular angreal Alivia was like 3x as strong as her natural strength when she faced Cyndane!

WH
With the Choedan Kal

Cyndane slowed at the sight of the woman standing among the trees a hundred paces ahead of her, a tall yellow-haired woman who simply watched her come closer. The feel of battles being fought with the Power in other places made her wary at the same time it gave her hope. The woman was plainly dressed in wool, but incongruously decked with gems as if she were a great lady. With saidar in her, Cyndane could see the faint lines at the corners of the woman's eyes. Not one of those who called themselves Aes Sedai, then. But who? And why did she stand there as if she would bar Cyndane's way? It did not really matter. Channeling now would give her away, but she had time. The key still shone as a beacon of the Power. Lews Therin still lived. No matter how fierce the other woman's eyes, a knife would do for her, if she really thought she could be a bar. And just in case she proved to be what they called a wilder, Cyndane prepared a small present for her, a reversed web she would not even see until it was too late.

Abruptly the light of saidar appeared around the woman, but the ready ball of fire streaked from Cyndane's hand, small enough to escape detection she hoped, but enough to burn a hole through this woman who—

Just as it reached the woman, almost close enough to singe her garments, the web of Fire unraveled. The woman did not do anything; the net simply came apart! Cyndane had never heard of a ter'angreal that would break a web, but it must be that.

Then the woman struck back at her, and she suffered her second shock. She was stronger than Cyndane had been before the Aelfinn and the Eelfinn held her! That was impossible; no woman could be stronger. She must have an angreal, too. Shock lasted only the time it took her to slice the other woman's flows. She did not know how to reverse them. Maybe that would be enough advantage. She would see Lews Therin die! The taller woman jerked as her cut flows snapped back into her, but even as she shifted her feet with the blow, she channeled again. Snarling, Cyndane fought back, and the earth heaved beneath their feet. She would see him die! She would.