No, the second meaning does not work. The word follow cannot have that meaning.
For contrast, let's look at a different sentence:
A dog chased the man into the store.
This sentence can have two different interpretations:
The man caused the dog to enter the store. (The man chose to run into the store, and the dog ran in behind him.)
The dog caused the man to enter the store. (The man was running to get away from the dog, and the path away from the dog led into the store.)
Why can this sentence have more than one interpretation? Because the word chase has more than one meaning, and the sentence does not make it absolutely clear which meaning should apply.
chase - verb (1)
a : to follow rapidly : PURSUE
// a dog chasing a rabbit
4 : to cause to depart or flee : DRIVE
// chase the dog out of the garden
The first interpretation uses definition 1a. The second interpretation uses definition 4.
For the purposes of our discussion, definition 4 is the more interesting definition. This definition describes a particular kind of relationship between the subject of the verb (dog) and the object of the verb (man), where the action of the subject is causing a certain behavior in the object. (That behavior is "running away".) In short, definition 4 is the only reason we can say that the dog caused the man to do something. If the word chase did not have definition 4, then we could not interpret the sentence that way.
Now, if we look at the definitions for the word follow in the dictionary, do we see any definitions similar to chase's definition 4? That is, do we see a definition where the action of the subject is causing a certain behavior in the object? No, we do not. There is no definition of follow that describes a situation where the dog is causing the man to enter the store.