No - on iOS 12 and lower, the device will not conserve data when you connect to WiFi.
Apple has previewed and announced that there will be a low data mode as part of iOS 13. This announcement was made at WWDC in June 2019 and also listed toward the bottom of this feature announcement page:
Low Data Mode
Apps on your iPhone reduce their network data usage.
You would need some more elaborate networking filter to reduce data usage via WiFi when tethered or just connected to WiFi today on shipping iOS. For now, the practical way is to closely monitor and manage your updates and settings so you don’t automatically update when connected to WiFi or ensure those downloads and syncs complete before you rejoin your hotspot.
You can use services to proxy or log data connections. Two I think are very useful are CharlesProxy and guardian firewall:
They both do more than simply meter bandwidth, but are trusted and clear how they generate revenue and are unlikely to abuse your data or privacy if you cannot wait for Apple solutions.