I would agree that it sounds awkward.
Our normal construct for this would be, "He's punctual." or "She's a punctual worker/employee". Saying that somebody is on time for personal appointments, such as dates or hanging out with friends is rarely described with this terminology.
In personal settings, it would likely be more like, "He's always on time", "She's reliable.". "They never keep us waiting".
Prompt action
Prompt delivery
Prompt response
Prompt aid
Prompt service
People are generally not prompt, We would say, "She is prompt with her response", or "She arrived promptly". You can say "they are always prompt", but not normally, "they are always prompt people"
Objects are not prompt. We would say "The train departed promptly at 1pm".
Hope this helps.