Aw, poor little sweetheart!
I'd absolutely say he's OT on nursery days. Not only is he napping short, but he's also very very stimulated while there! Lots of kids and new toys! Great and fun, but also exhausting!
Those EWs and tantrums are a very very OT bub waking early. It sounds like you're typically getting a 10 hour waking, which is always OT at our house. In fact, just had one this morning! Unlike a normal day, he wakes at the 10 hour mark screaming. I think they are frustrated because they are still tired (and my guy is 2.5!). You may also be seeing some night terrors -- with NTs they appear to be awake but aren't. They can even continue screaming while you hold them, and its because they are still in the throws of the NT.
Earlier bed on nursery days should help! And hopefully as he gets used to nursery, he'll nap longer which should also help. I wouldn't worry about the non-correlation of the nursery days and the EWs -- OT is cumulative and can just be more bothersome on some days and not others.