10-59 is a very wide spread. Mortality is much higher in the 50’s, then in the teens.
It is well known that the older someone is, the more likely they are to be vaccinated.
Controlling for age as a variable is obvious, and is standard academic practice. That they did not do it is a huge red flag for bias (or incompetence).
The control was there. The comparison was between both 10 to 59 groups.