I do not like to manage, especially with people my age (peers) or people older than myself (if they require much supervision which many don't and since I'll be 69 in a few weeks I don't have that problem any more). I don't know your qualifications but if it is a software projects; you should be more versed (skilled) than your temporary employee? Also perhaps following this discussion of Millennial and Gen X I may not be qualified to advise (And I'll Google those phrases and find out what da heck they are after this post).
OP you posted your whine - I try to give you some insight but you may not like it.
If the office is set up to work 8 to 5 with an hour for lunch and the require break then being on time is a given. Your rule of don't make a habit of being late for things a bigger problem like missing necessary deadline and that is either your supervision or the employees lake of experience (mentor) talent (your problem), skill(your problem) or motivation which you need to provide as a manager.
Do your work correctly also means he has to be competent enough to do his work correctly
If you agree to certain expectations - meet them also means that he is responsible enough (and competent enough) to fulfill those deadlines and all that goes with it.
Don't make me babysit your workday also means that if the person is just not proficient enough you have mentor; never babysit, it is counter productive.
Don't whine - children whine adults bellyache, complain or gripe (An immature adult that whines should be terminated with prejudice). The difference is subtle enough that some inexperienced managers nay not recognize it. To say this deadline is brutal is just a way to express oneself and bellyaching is normal and acceptable. Asking you once why do we have to adhere to this deadline is not whining and deserves a frank and truthful answer like that is what we committed to back when we took this contract. Asking the question again a week later is not whining it is saying the problem still is getting worse and politely implies you are not doing your job. Coming to you and saying we may not be able to meet the deadline as your other employees may if this weak link is putting you off schedule is really saying you as a manager you really need to do something (besides whining on this forum).
The few times I've been stuck in a management role I have led by example.'
Don't make a habit of being late for things. If work begins at 8:00 I show up before anyone else. If I had a subordinate who also shows up at 7:45, I show up at 7:30. I tried to always be the last to leave. If we have an all hands type meeting I arrive at least five minutes and am prepared. Be punctual in all that you do to set an example.
Do your work correctly. Some people follow what we used to call the peter principle they rise until they reach a position they can't handle. This may well be this person but if so; it is your problem now. I found a way to work around that and still get the job done.
If you agree to certain expectations - meet them. If they can't handle that requirement; it is your problem now. I encountered that and still got the job done often without ruffling anyone's feathers.
Don't make me babysit your workday - you don't babysit you supervise and if needed help, mentor or assist but never babysit. If you think you have to babysit; the problem may be you. Fortunately I've never had to supervise anyone I had not mastered the task they were trying to do. I would mentor and show them the tricks I had learned and usually got great results; then again I would never take a job I couldn't replace, demote, return to a place they were competent or terminate. I may not have had the direct power but I wouldn't take a managerial task if they wasn't an agreement with higher supervisor who had the power replace, demote, return to a place they were competent or terminate, Usually a high muck-e-up who was displeased because other supervisors weren't getting the job done and since I had duties and was getting my job done I was asked, not tell, see if I could solve a problem. I would say I will assuming if I have a problem (Like you do now) you'll take my judgment and take the necessary actions on my recommendation.
Don't whine. Complaining isn't whine; adults don't whine so either get thicker skin or realize the problem is probably your attitude. If your personnel complain fix the problem or explain why you can't. It usually took me about three days to solve most complaints after I was thrust into a managerial position. I say adults don't whine; you may be an exception to the rule.
If it is your problem now you have your job cut out for you. You say you can't terminate or demote this person out of your working group so you may have to do his work because completing on time is your responsibility and your job.
Since you don't have the power to replace him you can continue being a jerk and ride this guy for not making his deadline and not adhering to your set of rules and maybe you will get him to quit or maybe your superiors have the power to replace him will solve the problems; which could be replacing him with another and moving him back to the job he was doing. The problem with that is you attract attention and you better be accomplishing the ret of your job or solving the problem may be as simple as replacing you.
You have three ways of doing your job: You can supervise and get the job done, be a BOSS (spelled backwards is double S O B) an get the job done for a little while. or be an office controlled by the sphincter muscle until you fail as it appears you're setting yourself up to do.