Is there a way to prevent background application updating on both wi-fi and Mobile Data?
You can define that hotspot as being a "mobile hotspot", so Android would deal with it as if it were using mobile data:


Open Settings
Go to Data Usage
Tap the "overflow menu" (the 3 dots in the upper right)
From the menu opening, select Mobile Hotspots
Put a check-mark next to the hotspot you're using.