Yes if they have any other kind of income.
The threshold you have been told about is the Lower Earnings Limit for National Insurance, currently £116 per week.
www.gov.uk/guidance/rates-and-thresholds-for-employers-2018-to-2019#class-1-national-insurance-thresholds
IF the person had no other income of any kind and not have any more income at any time whilst working for you, then you would not have to register as an employer.
If they have other income, however small, you will need to do full payroll (PAYE). Due to the low pay, you would not be paying any employers National Insurance. You would not be deducting any employee National Insurance either. You may though be deducting Income Tax from your employee, as that is dependent on their total earnings from all their income.
As your employee, they will be entitled to paid holiday. If they are working term time only and cannot take that holiday during term time, then factor in that you would pay that holiday for a period of time during the school holidays.
If they worked 3 mornings per week, 38 weeks per year, then that is 3*38=114 mornings per year. Holiday added on would be 12.07% of time worked, which is 12.07% of 114 = 13.76 mornings. This can be rounded up but not down.
To put in money terms, if paying £22 per morning...
£22x114=£2,508
Holiday added on = £302.72 (12.07% of £2508)
Giving total of £2810.72