YOU are in charge of how the client (or their staff) treat you. People will walk all over you if you allow them to. But they will also learn to plan better if you refuse to let them. So it's your choice how you want to "train" your clients.
During initial exploratory conversations with clients, I make a few important facts as clear as I can:
I do NOT, by default, work weekends. At no time should the client anticipate or expect that the coming Saturday and Sunday are working days for me. The only way I may work a weekend is if arrangements have been made prior to Thursday of that week... and even then, I may not be available for that particular weekend.
I never accept "overnight" projects without additional rush fees. If there's a typo or error on something, I'll fix the error as soon as possible, which may often mean same day/overnight. However, I do not ever initiate a standard new project for an expected overnight delivery. At a bare minimum I require 36-48 hours notice for anything. And that does not ensure I can complete things within that 36-48 hours. It merely ensures I'm aware that the project is needed rapidly. A rush fee may be available depending upon my current schedule if a project truly is needed. This may mean overnight delivery, if the scope of the project makes it even feasible. (I can't do 40 hrs of work "overnight")
The only thing I can't change are the amount of hours in a day. I have other clients and other projects. My time is a limited resource and I must schedule things appropriately so that expectations of delivery are possible with all my clients. As with any business, I constantly market myself and constantly acquire new projects. Things are completed on a first-come-first-serve basis. Understand that I want to get everything done as soon as possible. However, that is not always achievable due to physical demands such as sleep, food, etc.
I don't answer calls or respond to emails after standard working hours. If there's truly an emergency, they can call and leave a voicemail. I may check voicemail after hours and be available to address something which is actually an emergency. However, emails may not be seen until the next business day and voicemails not referring to an actual emergency may not be addressed until the next business day as well. This holds true for weekends as well... I may check voicemail over weekends, but I probably will not be checking emails.
99.9% of my clients understand all this and really just see it as common courtesy. They may tell me they needs something "NOW" but they all understand that their "now" means "as soon as I can" for my business.
There's an old saying, "An emergency on your part does not constitute one on my part." Now, I don't actually recite that to clients, but that's what I think.
If a client asks for something which is not feasible, I just reply with "Sorry, I've got a lot on my plate at the moment. The best I could do is get this to you by XXXXX. I understand you need it as quickly as possible and if I can deliver it sooner, I certainly will. I just don't see how I can get this done by XXXX due to prior commitments."
Almost without fail, the client understands. However, If that statement causes issues, then I explain that there's little I can do. And while I realize that something is imperative to them, I have additional responsibilities which are important to my business. I can't simply drop everything to complete their project.
Sidebar... if I'm being repeatedly pushed by "employees" or "staff" of my client and I've already reached out the client about problems with demanding deliveries from staff, then I'm just formal and blunt with the staff... "No. I can't do that. The best I can do is have it to you by XXXX." If they argue, I merely state... "Sorry. My schedule is booked. If there's an issue with this please have [the Boss/My client] contact me to discuss possible escalation incurring additional rush fees." I've lost track of how many times the "expected delivery" has changed to a more reasonable timeframe after such exchanges.