Pearson told the Pinkerton where to find John.

In the end credits you see the Pinkerton looking for Dutch's gang. They start in valentine and slowly make their way to Rhodes.

Also during the end credits, you see where some of the remaining gang wound up. Tilly is seen walking with her husband and child, Mary Beth is writing at a desk, etc.

When they show Pearson, he's attending a customer at his store and then he stares at a portrait on the wall. It's a picture of the whole Gang. Dutch, Arthur, and everyone else.

Soon after, the Pinkerton are clearly shown investigating at the entrance of Rhodes. Meaning, they've possibly found Pearson.

If they walked into the store, they would see the gang's portrait. They would get to asking questions and we know the following:

*Pearson knows where John lives. John told him because Pearson wanted to write him letters.

*Pearson's domineering wife didn't want John in the store because according to Pearson, he got too drunk on Rum and told her too much about the gang and their old ways.

*Every time there's an interaction with Pearson and his wife, it's always her screaming at him and Pearson cowering to her demands.

The next cutscene, the Pinkerton are now at John's ranch looking at him though binoculars.

Pearson was questioned and possibly threatened by the Pinkerton. His domineering wife forced him into answering questions and revealing what he knew.