Great question! This is a minor issue, I guess one of taste, almost. I don’t think there are super clear guidelines on what having a period vs none indicates. It’s all speculation from there. Some think the period gives the reader “closure” about the title as a unit.
Personally, I think it’s misleading. The subtitle is not the first sentence. It’s a title. A subordinated one but a title still. And titles don’t have punctuation. It’s easier for me to understand the title-sub combo as a unit if neither has punctuation. “This is the movie, and that’s the tagline, got it.”
But again, mostly a matter of preference, I think!