None of us can help with this because we don’t know the culture at your place of work, and nor does OP know all the details. I think the OP needs to realise she has limited understanding of all of the intricacies of her team and needs to adjust her expectations based on this.
Reading between the lines it seems the OP seems to think the only response to “jump” from a junior member of staff is “how high”, and respectfully I think office culture has moved on from those days for the better. Particularly for women.
It could be that he’s lazy or he could just be busy and trying to manage expectations. I actually quite like the way he’s politely and tactfully tried to push back and has been honest about his availability. If I was OP I would have tried to understand what he was saying and ask someone else or adapt.
When I started my current job when I was much younger and more junior, I had a micromanager who was a complete nightmare to work for.
Every second of my time was accounted for, he had to know what I was doing at all times and sometimes I would be sent a quick follow up question or task from someone else to do with previous work I had submitted. He used to sit next to me and look over at my screen and if he saw something he didn’t expect, he would start with the questions.
”What are you working on? Why are you in that file? Who had asked you to do this? Why are they asking? When did they ask? How long have you spent on it? How long will this take? CC me into your response.”
So if someone asked me to do something, even if they were senior to him, I would run it past him out of principle and play him at his own game even if it would reflect badly on me (or him), because he was such hard work. The OP doesn’t know what it’s like to work under her direct report. Everyone above my manager loved him, and had no idea of how difficult he could be to those who were “lesser”.
If I ever had a week of leave planned, I would usually have to do two weeks of work in one, and I would be absolutely hammered to the point where I probably wouldn’t have been able to comfortably assign 15 minutes to do something else, particularly on the last day. I remember being in the office pre-Covid at 10pm on a Friday night and being close to tears because I thought I was going to have to cancel my holiday the next morning because I had so much to do. I didn’t but I spent the whole week fretting and sobbed on my way to the airport when the holiday was over. I was earning 25k at the time.
We would also have a lot of tasks come in at the last minute and you can guarantee that if you ever had a dentist appointment or train booked, one would come in that day. I remember having loads of half days booked but in the end leaving only 1 hour earlier than I would have done anyway.
We also don’t know if this is actually a 15 minute task, or if the reality is it’s a lot more. I have a manager (not direct) at the minute who has crazy ideas of how long things take (she estimates a day when three or four would be more appropriate). Some people just don’t understand.
A lot of OP’s responses read like she thinks the culture is the same as it was 30 years ago. It isn’t and it has changed for the best, in my view.
Our grads are sometimes a bit green (as expected) but they all mean well and I feel for them because I remember what it was like to be thrown in at the deep end.