The first sentence is Conditional type 3 (refer Articles - English Usage Articles - Third Conditional in this site.) Here you imagine a past situation which didn't happen:so, in the first sentence, the person didn't leave the train a minute earlier and the police didn't catch him.
-In the second sentence You imagine a possible past situation.
Here you don't want to express certainity as to your father trying to catch you when you took first baby steps. Because if you do, then you could have used "will" to refer past instead of would, as in:
When I took my first baby steps, my father will have caught me.
keep in mind though, choice of would or will depend on how certain you are about what you want to say.
Hope I have given you some food for thought.
Student or Learner