This systems don't install themselves, nor do they install themselves in surreptitious ways. The examples you gave would basically boil down to the applications installing themselves illegally via hacking. That is incredibly difficult in practice, would put a legitimate software company out of business, and a workplace certainly wouldn't use illegal methods to get such software installed.
So how do they get it installed?
Most importantly, you will sign paperwork as part of your terms of employment stating that you agree to install the necessary security software/business software/whatever that is needed for you to do your job, with the company deciding what is necessary (of course). Then one of two things will happen:
- They will install whatever they need on your work machine before sending it to you
- They will ask you to install a remote management system, which will then install/remove any additional software as they see fit.
Note that regardless of how it gets there, once the remote management system is installed the computer is, in essence, no longer yours. Such things should really only be installed on work computers. For any number of reasons, you really don't want to be using personal devices for work, whether phones, desktop computers, or laptops.
Hopefully your company isn't asking you to install this on your personal devices. That would be a deal breaker for me, but depending on your industry and country, you may not have much of a choice. In that case you can do yourself a favor and buy a cheap device to use exclusively for work (if possible).
Still, unless you have specifically installed something on a personal device, you don't have to worry about such "spy" software being on it. There really isn't anyway that such software can automatically install itself on your personal devices, even if they share a network with work devices that have such software installed.