You don't need to control the spell or ability that creates the tokens, nor do you have to be the one creating the tokens for Chatterfang's ability to apply. As long as the tokens are being created under your control, Chatterang's replacement effect will apply.
Chatterfang's second ability applies to all kinds of tokens, including Clue, Food, and Treasure tokens.
If an effect changes under whose control a token would be created, that effect applies before Chatterfang's effect applies. If an effect changes under whose control a token would enter the battlefield, that effect applies after Chatterfang's effect is able to be applied.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Jason A. Engle
Card data via Scryfall. Rarix is fan-made; not endorsed by the rights holders.
In a Commander game, the defending player is the player Chatterfang is attacking or the controller of the planeswalker Chatterfang is attacking.
The additional Squirrel tokens won't have any abilities the other tokens were created with. Anything else specified in the effect creating the token (such as tapped, attacking, "That token gains haste," or "Exile that token at end of combat") applies to both the original tokens and the Squirrels.