Real protective glasses won't just have the "opposite colored" lenses for protection, those are probably cheap crap and nothing more.
For example I have never seen red glasses for 532nm (green) lasers, they are usually orange(-ish) and quite transparent.
For example mine are the darkest I've seen, and I've seen many green laser glasses:
With your glasses you should get some kind of technical specification/declaration of conformity, stating all the affected wavelengths and the level of protection at those wavelengths, and as expected it should cover also the auxiliary wavelengths that blueskull mentioned (with Yb:YAG you could be pumping with 940nm)
I've seen many manufacturers of these laser protective glasses, just google and see if they state technical specifications clearly for their products. I definitely wouldn't go the ebay way, but just as a warning I've never paid less than 100 USD for any of my protective glasses, but mine are "medically approved" meaning extra charge.
Now, having said all of this, you won't be able to do a damn thing with those glasses. Since you mentioned you want to bounce them off of mirrors it means you'll have to align the mirrors, and you don't see the laser if you have your glasses on, so your option is to risk it or use a pilot/aiming beam (in your case a weak green laser if the main one is red). Using a pilot beam adds complexity to your project because it takes some good planing of the beampath to align it with the main beam.
I usually risk it, except when touching the beampath of the CO2 laser or moving around the KTP in the 532, since it might bounce off of whatever I'm using to move the KTP.
P.S.
If you're into lasers and near Munich on June 26-29, there is a fair there: "LASER World of PHOTONICS", some really cool and nerdy exhibitions every time.