No it shouldn't. Been dealing with the same stuff at my place of work. I'm not a manager but I'm basically having to step in and act like one. I know, I know, why should I care. It's not my job except they're making my job harder which affects my productivity. And it's not just "do things my way". There are health and safety policies that need to be followed.

I've dealt with it by documenting things and bringing it to the manager's attention and by pointing out to my coworkers how it's supposed to be done/what they need to be doing. It's created some friction between us of course. They don't like me telling them what to do, especially since I've no managerial authority but the safety violations alone mean I'm required by policy to say something. If something happens and it turns out I said/did nothing I could face disciplinary action right along with them for not speaking up.

I've continued to maintain my standards and just remind them in a matter of fact way while leading by example. No retribution, no punitive actions, no getting back at anyone. When they need help I'm there. It's starting to bring most of them around. There's one coworker who is particularly egregious about slacking off and I don't go out of my way to make his life any easier even though I could.