Albon, who will partner eight-time grand prix winner Verstappen at the main Red Bull outfit in 2020, had endured a topsy-turvy pre-F1 junior career that included a difficult three-year stint in two-litre Formula Renault and an exit from Red Bull's junior programme.
He had begun 2018 without the budget for a full season in Formula 2, but ended it with a Nissan Formula E deal, which he then swapped for a late Toro Rosso call-up that yielded a subsequent mid-season promotion to Red Bull.
Asked about the expectations for Albon's 2020 campaign on the heels of what is a rare straightforward off-season for the Anglo-Thai racer, Horner said: "It's probably the first time since his karting career that he's had that.
"He'll only benefit from that. He's had a lot of adversity to deal with during his career.
"And I think, you see people's make-up in adversity and I think he's shown that determination, that character, and I've got no doubt he'll benefit from stability now.
"And he shares many of the same virtues that Max has with that ability to cope with pressure, that determination."
Though Albon has so far not run Verstappen that much closer than his Red Bull predecessor Pierre Gasly, he proved a more consistent points-scorer and more adept in race trim, and was only denied a maiden podium in Brazil by a penultimate-lap clash with Lewis Hamilton.
"There's no specific goals [for 2020], he's just got to continue his development," Horner said of Albon.
"You've seen every race he's done with us, he's just got better and better. And I mean, he was unlucky in Brazil, but I think he's driven brilliantly well - first year, two [different] teams plus the pressure of coming here and having Max Verstappen as your teammate.
"He's handled that really well. I think he's impressed the whole team with his approach and his attitude, with his feedback, with his pace that continues to grow."