Isn't that violating the lightspeed limit?

It's not so much 'violating' the lightspeed limit as laughing in its face because it isn't constrained by it. Stuff within space travels at or less than the speed of light, space itself can do as it pleases (as determined by weirder stuff than just special relativity).

As you describe it, there's a frame of reference in which Alice and Bob are moving away from each other faster than the photons they are traveling near.

I'm not sure on the appropriate terminology here. Do they call it "moving away from" when neither thing has moved but have simply become further away from due to space changing?