The text says Dixit and Madhavrao decided to postpone their trip because the train was full. Does this mean they actually went back and traveled the next day?

No, they did not end up postponing their trip. While Chapter 51 states that they did decide to return and go to Shirdi the next day due to the second-class compartment being "packed to capacity," this was not the final outcome. The text immediately follows this by explaining how the situation was resolved. Just as they were gripped by this worry, the train guard, who was an acquaintance of Dixit, appeared. He made an arrangement for them to travel in the first-class compartment without any issue. Therefore, as detailed in Chapter 51, they continued their journey to Shirdi that same night.