Interesting, what's your objection to that? Seems like a reasonable way to make a request to me. Also seems reasonable to agree to or deny the request.
Not the parent, but my objection to that would be that your feelings are yours to handle, not me. And for this kind of request, saying that you feel disappointed because I don't have time to finish the tickets will definitely backfire, with a "you should adjust your expectations", and using emotion talk in this context will immediately frame the talk as manipulative.
Would it then be preferable for the manager to be more direct and assertive and state "In order to continue being employed here, you will need you to work overtime."
To me there needs to be a differentiation between communication style, and consequence. If it is the case that your job is at risk unless you work late nights, is it preferable to be direct about it, use assertive language, or is it preferable to use NVC, and express ones feelings and other details that form some sense of empathy?
My personal objection is that it purposely confuses things.
It's worded in a way that connects declining with not being a team player. Obviously that's an intentional construction and to some people it makes perfect sense. It also is emotionally manipulative because it intentionally seeks to manipulate the receivers emotional state so that they comply. Some people will comply to resolve that discomfort. The inherent power imbalance distorts the situation.
It also confuses the language of personal relationships (affective statements) with the workplace. To me, this is in the same realm as getting employees to view the workplace as a family. Again it hijacks the our relationship cognition centers in order to engage in exploitation. Declining in a regular relationship has regular relationship consequences. Declining this kind of statement from a boss has livelihood consequences.
The solution in the workplace? Just say it plainly. Bringing NVC into the workplace is fertile ground for emotional manipulation.
If I heard this, I would think that those words are coming either from a sociopath or from a very socially inept person who read a self-help book. There are probably cultural differences in how it's perceived but it sounds so fake, forced and manipulative that it would make me put my defences up immediately.