Honestly I don't know. Considering Thrawn was the only Chiss that served in the Empire (well Palpatine's Empire, there were plenty that served the Sith Empire during TOR's time) and considering he was the only Chiss we'd ever met prior to The Old Republic being released I'm pretty sure his species and Thrawn himself were thrown out with the rest of the EL (also, Thrawn was never mentioned in the movies so as far as Disney would be concerned he doesn't exist in the new canon. He was only in the books and games (serving under him in Tie Fighter was awesome)). It'd be completely awesome if Thrawn just randomly shows up in the next movie, bitch slaps Snoke, takes control over the First Order and then completely wipes the floor with the Resistance (yea, I'm an Imperial groupie). Yea it won't happen but a man can dream can't he?
I've never really read the books so I only know his personality and characteristics from Wookiepedia and what my friend told me about him. I know his men followed him unconditionally due to the respect they had for him, he was a true Imperial and would do anything to bring it back to prominence and his men understood this. Plus he always rewarded those who tried, as you said, to follow there orders to the best of there ability. He never outright killed anyone for disobeying or failing him like Vader did (which is why Vader had complete control, as awesome as Vader was he wasn't exactly the more inspiring man in the galaxy). My thing is that considering how the EL was thrown out the door the Empire at the time of it's defeat was extremely xenophobic which is why you never saw any alien officers or stormtroopers (Thrawn was the one exception). By the time of his rise to power what was left of the Empire was more accepting and allowing aliens to freely join which is why I think he became the figurehead they all were drawn too (plus the whole being awesome thing helped a lot). Hell the 501st legion, a legion made up of entirely clone troopers that had served with Vader during the Clone Wars and after, started letting in aliens and rank and file humans into it's ranks around this time but that's neither here nor there. At the time of Palpatine's and Vader's deaths no one would of followed him except those under his direct command which is why he'd of had to of been more ruthless then he actually was to take control of the Empire.