If the person is able and willing to surrender after being shot, showing their hands (empty of anything they may have been holding before) and following instructions means the police can start first aid and bring in EMS sooner. The ambulance doesn't come in until it is safe to do so which won't be until after a search is done and handcuffs are applied. Specific details beyond that and exceptions to the norm would depend on local policies.
Assuming there was ever anything in the victim's hands to begin with. Plenty of cops will go on to deny the person emergency treatment under the guise of the individual being "too dangerous"
Edit: To anyone daring to question the veracity of this statement, just go ahead and watch the last moments of this man's life then take a good long look at yourselves and think about just what you're trying to defend here. This is nothing but murder. Decided on by an overly-sensitive EMT and endorsed by six different cops. Be ashamed of yourselves.
Just a guess, but I'd think it'd be based on fault. If it's a justified shooting, they'll probably tack it into the suspect's fines. Ideally, if the shooting isn't justified, the govt would pay, but I wouldn't count on it.