everything I've read is you check the reservoir level when it's cold and everything is parked in it's... correct state for the check. Hydraulic fluid expands as it gets warm, my Dad's kubota will go from right in the middle to over the top of the gauge. Apparently it's done this since new, and other people with smaller (8k) kubota mini ex's say it's normal. My Deere raises my level by about a half inch when the rig is warm vs cold.
you say yours drops the level below reading... I dunno! Does it work as expected? Oh! Thinking about it... my 50 ex, my Dad's Kubota - both of them have the reservoir above the pump. Or at least the top level of the reservoir is above the pump and all the big lines. Is the reservoir of the Terex lower on the machine compared to the engine and pump? if so, it's draining back to the tank when it sits overnight - and Terex likely designed it that way. if they didn't want that to happen, they'd have put in a check valve or put the reservoir somewhere else.
I dont know man.. I've never even looked at a Terex - they just don't have them around my area. this is Cat country with a bit of Deere, Doosan and Kubota mixed in. Just no Terex - I've seen a Terex dozer... 1 in about 5 years. big, green & ugly. but probably a hell of a machine!
Looks like you can get a manual from here:
https://en.terex-club.com/manual_download.php?id=236
By the way, looking at the boom design on these:
https://en.terex-club.com/model/terex-tc50-151 these look like nice machines! congrats on getting a well thought out rig. I wish my lower hydraulics were protected on my boom the way yours are!