The 26-year-old was traded to the Bills from the Tampa Bay Buccaneers for a sixth-round 2014 Draft pick, which followed an off-the-field incident where Williams was stabbed in the leg by his brother.
"Yes, I think I do need to grow up a little bit more," Williams told the Buffalo News. "I think with me having a son, it made me realise things a little bit more and how important it is, and what type of future I have for him and my family.
"A lot of people are depending on me, so you're right, I do have to grow up."
Williams recorded 22 receptions for 216 yards along with touchdowns in six games for the Buccaneers last season.