The EMV standard supports two (technically three) methods of verifying a PIN. In the first method ("online"), the PIN is encrypted and sent to the bank for verification. The other method ("offline") asks the chip to verify the PIN, and only the result is transmitted to the bank. (Offline is further subdivided into "encrypted" and "plaintext", depending on how the PIN is transmitted to the chip, but the practical differences are minimal.)
In general the banks in a given country tend to be all online-PIN or offline-PIN. In the US, which it sounds like you're in, most cards are online-PIN. Thus, changing your PIN via the bank's website or app will immediately take effect, without having to update the card.
Additionally, there's a specific EMV tag that a bank can return to the terminal to pass on to the chip which can update the PIN stored in it. Not all terminals support it (the feature is called "issuer scripts"), and it doesn't work with contactless or "quickchip" transactions (because the card is no longer present when the response is received), so I don't know how common it actually is - but it does technically exist, and was presumably used at some point in time. It's probably more commonly used over the ATM network than the credit card networks.