Will a software update in another partition (different OS) affect another, or overall

Good day.

Recently, I just installed 10.6.8 on an external drive because I needed to work with some PPC apps.

So, when I clicked software update there, it said that I had a Thunderbolt software update 1.0. And I installed it.

I don't know whether I screwed up or not, but will it affect the Thunderbolt chip, or just Snow Leopard? Because before my Macintosh HD was in 10.8, I had installed the Thunderbolt update 1.2.1 back in 10.7.4.

So after installing the 1.0 Update in the SL side, I'm not sure whether it would roll back the 1.2.1 update that was already in the Macintosh HD side.

Thanks.