Wow, a thread about Chabad Minhagim? This never happens.
They do indeed have a minhag to spit when they mention idolaters in the aleinu. Mentsch, if the only minyan near where you work is Chabad I’m going to assume it’s not a frum area/real community. If you go to a real Chabad community, you will see this.
I’m not sure why old shuls having dirt floors would matter. The issur of spitting in a shul goes back farther than Chabad has existed, I believe. But, then again, I would say that about zman hatefillah also, so what do I know?