I think Thiago looked shite because of injuries and getting used to the tempo of the Prem. Also, he's not a DM. He's a classic CM.
I don't know if the Thiago comparison does Morton any justice, because let's be honest here, Thiago is world class. Morton isn't anywhere close to Thiago obviously. I think he should just be in there grafting and getting stuck in.
Yes, he gets some leeway because playing in midfield is a lot harder than playing on the wing for instance.