My mentors made me do all the paperwork for the ensembles I taught, and when I started a jazz band I had to handle the fundraising ground up. I ran a solo contest for our (very large) MS for years, coordinating schedules, judges, food, etc. They were all available for questions, advice, help, and occasional correction.
Sometimes it was overwhelming, but I was able to walk on to my first HD position with 0 worries or knowledge gap on the administrative side of the gig because of how they worked with me.
In your case, I’d set aside about 30% of what you do, and take the time to teach your assistant how to do it. Then expect it to get done. Support / scaffold them like you would an advanced band kid, and remove supports as necessary. They’ll grow, and your program will benefit.