What is the umpire’s responsibility with regards to safety?

It is not the umpire’s responsibility to administer first aid. It is their responsibility to stop the game if someone is injured.

The umpire is responsible for the safety of all players and officials within the confines of the pitch. The umpire should ensure that the rules of the game are adhered to with regard to dangerous play and that play is stopped in the event of an injury.

The pitch is the area within the white lines. The home club would be responsible for anyone watching.