Trivia: When Casey enters the shop, the female store clerk is watching the TV. On top of the TV is a piece of memorabilia from The Iron Giant. The director of Tomorrowland, Brad Bird, also directed The Iron Giant.
Trivia: Michael Giacchino, the film's music composer, has a cameo as the operator of the It's A Small World ride.
Trivia: When Casey's hand is stuck in the force field, an action figure of Mr. Incredible from The Incredibles floats along the force field. This movie and The Incredibles were both directed by Brad Bird.
Answer: He was using it as a metaphor. The Titanic being mankind heading towards its own destruction. Man was warned of the dangers (wars, global warming, etc) and we didn't do anything to change our ways, "went full stem ahead".
Bishop73