Supergirl said his words. He realizes this soon after she says them, but he doesn't see any hint of familiarity with his first words from her. That's fine. He's been through this before, it doesn't matter that yet again it was no match. So what if he insults her on television later by stating Superman saved him instead, it's not because of that. Alright, it's a little bit of payback - a dick move but he's done worse for a lot less. He tired of the question, tired of waiting for his soulmate. He's waited his whole life, hearing the question several times in his life but never matched them with the speaker.
After his parents died, the little hope he had was held for her (or him, whomever it was). But after thirty-some odd years of waiting, he's lost the hope. If he hadn't met them by now, he doubts he'd ever will. He's read that it happens, sometimes, especially with common phrases and greetings. They go unnoticed or unmatched until they die.
And it's not like Supergirl didn't have time to react to his words between freeing him and Reactron arriving and blasting her out of the room. She was a bit busy after that, so maybe he'll forgive her for it. But she's done a lot of damage to and around National City, and he expects she'll do even more. He can't let that go; too many already do that for Superman and he's not going to have that happen in his city. Not when innocent people could be killed by falling debris or some supervillain interested in taking out Supergirl.
She saves his life again, later that night and he jokingly states he should put her on his payroll before leaving the scene. He stays far enough away to study her from a safe distance or at least he tries until that Jimmy Olsen character distracts Reactron and heads out of the building forcing everyone to run. But seeing Reactron again gives him an idea: testing Supergirl's abilities would be a smart plan. Learning her strengths might indicate some of her weaknesses. It might just help him figure out her secret identity. He already has an idea on how to do just that.
He can't wait for the fun to begin.