I have the same problem, too.
Fact is, I didn't have the chance to talk to Tarquin on ship when we arrived at the mainland:
He just walked to the boat and disappeared.
Later I checked out Stonegarden entrance where he was supposed to be, to get the quest started,
but he wasn't there.
Interesting fact:
Either after entering stonegarden OR after killing Qanna, he suddenly appeared by the boat on Lady Vengeance. But only trading was possible with him, no quest :(
I checked if after I talked to him, he would spawn at Stonegarden, but no: He was still on Lady Vengeance.
