Horford is listed at 6 ft - 9 in, Tillman at 6 ft - 7 in, but I don't think length is the issue. Horford is a career 38% 3-point shooter, 42% last season, Tillman is career 28% from 3. Tillman has a career 57% FT%, Horford 76% FT%. Tillman has a long way to go if he wants to be the next Horford. That doesn't mean he won't be useful productive bench player though.
I think there is a lot of truth in the assumption that it can take a season for a player to fit in, to find his role with a new team. That is especially true when the team is established and contending for a title, like the Celtics. Just look back on Derrick White in his first half season in BOS. We shall see how this plays out for Tillman this coming season. I do expect him to be better and he should get some real opportunity to start the season with Porzingis out. But he needs to find a way to score, or at least be a threat to score, or the other teams will just sag off him and clog things up.