It's a happy - well, happy if she manages to save Wolfgang, not so happy if she gets killed by a spider - accident that she stumbles upon the spiders at the same time Wolfgang does. She's on the rooftop when she sees both him and them, because she only ventures down to street level when she has to. This method has it's pros and cons, but she's still alive, so she's sticking to it. She recognizes Wolfgang, but even if she didn't know him she'd still go to help.

There's no hestitation once she sees one of the spiders go after Wolfgang, Steph just jumps down to a first storey balcony, getting her in range, then she fires her gun at the spider that shot the web. It's an energy gun, rather than one thatshoots projectiles, and if it has no effect on the spiders she's got an exploding batarang ready. Privately, she's relieved that she's not arachnaphobic, that'd make this more difficult.

At the very least, though, this is confirmation that the spiders are real.