Does Exchange enable MDM automatically on iOS?

I'm not sure if it could be done automatically when you sign into an exchange account. If your device is under MDM policy you will find a configuration profile in the Settings.

How to delete a configuration profile on iOS

1. Open Settings on your iOS device.
2. Go to the section General → Profiles & Device Management, or Settings → General → Profiles.
3. Tap on a configuration profile you would like to remove from your iOS device.

4. Tap Delete Profile at the bottom of the configuration profile screen.
5. Enter your passcode, if required.

6. Confirm that you would like to remove the selected configuration profile from your device by tapping Delete. When you delete a profile, all of the settings and accounts associated with the profile are also removed.
7. It is always a good idea to restart your iOS device after removing a profile.