HTML select element – dropdown keyboard expected functionality

Wanted some opinions on using HTML selects for keyboard input. We're developing an app in React using Material UI, and their version of a select dropdown element is pinging a few questions in testing.

The Material UI SelectField operates as such with keyboard:

https://www.youtube.com/watch?v=swz82ul6Hao

A browsers default action is as such:

https://youtu.be/MCaDh9JlIr4

I note that when you tab to the input and activate it (enter or down-arrow) in the default browser version, the currently selected item, or the first default item is focussed - whereas with the Material UI version, you have to press up or down once its activated to get any item focussed...

Any thoughts on this?