RE: 2 users executing the same automation script?

I am assuming you asked about execution the same script on TIC server. You should not have any issue as soon as a backup person has manage right on the script. To grand manage right you have to do the following
1. Select the script on Object Explorer
2. Press Share Object
3. On Alter Visibility dialog select Share this data with selected users
4. Find the backup user and add him to the left side and select Manage check box for him
5. Press Show Script
6. Press Execute 

Regards
Aleksey