When you sign in on a device with your password, all (encrypted) keys will be downloaded to your device and decrypted with your password. While the app is running, the decrypted private key is kept in memory and can be used to decrypt your files.
Changing your password on a device does not affect any other device you're currently logged in. If you want to explicitly unlink all other devices from your account, you can do that here:
PS: On any new device you always need the latest password to sign in to your Boxcryptor account and decrypt your data.