Pippin asks, "Do you think we'll be pursued tonight?" Tom says, "No, I hope not tonight, nor perhaps the next day", but don't trust his judgement because "out east" his knowledge fails. His thought is rooted in hope. Indeed, don't trust his judgment because they were in fact pursued that night. He's correct that his knowledge fails "out east" because that night, they would have ended up dead, save for Nob and Strider. The hobbits actually walked right into (another) trap. Tom adds that his advice is "good...till this day is over" and it was, but after that, they should trust to luck. I think this suggests that Tom had no real knowledge beyond his borders of where the Nazgul were searching. Out "east" must mean anything east of his borders. None of the Nazgul were actually in his country, where he is master, but were all beyond, where his mastery/knowledge ended. I reckon he knew the Rangers had been protecting the Shire and likely were on the lookout for them. Earlier, Goldberry had discerned their sleep was disturbed (or perhaps her spell was working on them in their dreams), but I wonder if Tom discerned Frodo's dream of Gandalf racing to them. While Tom didn't know how help would come to the hobbits, I suspect he wasn't worried about them because he knew the Bagginses were endowed with an extraordinary amount of ...luck, as it's called.