1. Set the default site email in: 
   Configuration > System
   This default has to remain the Upsun-generated email 
    
2. Set the default Webform From: address in:
   Structure > Webforms > Configuration > Handlers
   This default can be whatever email you want, for your department 
    
3. If desired, set a default Reply-to: address on the same page as #2. 
    
4. If individual forms need a different Reply-to: address, change it in:
   Structure > Webforms  > [form name] > Settings > Emails / Handlers.

These steps should prevent emails from your Webforms from being flagged as spam, which often happens with the Upsun-generated emails