But most importantly: the also liked Vito.
Yes, but at the end of GF, Tessio, turned traitor, said: "Tell Mike it was business. I always liked him."
I think Clemnza liked Vito but I am not so sure about Tessio. Clemenza was an extrovert who enjoyed his food, his wine, his dancing and his wife and kids.
Tessio, the smarter one was purely a businessman looking out for his own best interests. As soon as he thought the takeover by Michael was a done deal, he figured the Corleones would be toast and he turned traitor. I don't think that thought ever crossed Clemenza's mind.