I see no reason to believe anything will change, especially not immediately.

I’ve yet to see any indication that she’s become anymore powerful than she already was. Not that flight is any small feat, but she could already self-levitate. Everypony in Ponyville already knew she was Princess Celestia’s student. If ever she called out, everypony in town already listened and was ready to act when necessary. It might seem different, but ask yourself what’s really changed.

The biggest adjustment for anypony to make will be for Twilight herself. Her personal identity has been altered. We’ve always known who Twilight was, even if only subconsciously. She’s the one that’ll need to come to terms with who and what she really is.