submit content to other sites

No problem. You can use your photos however you wish.

To be clear, you also need to be sure that other sites you upload to do not claim exclusivity.

If you created the asset you won't have any problems; you can upload to as many stock sites as you wish. Abode don't have exclusivity, unless you you agree to it. But that's a different situation.

Adobe acts as your agent and when one of your assets is downloaded, it is licenced by your agent (Adobe) for use.  However the copyright remains with you.  Yes you can submit the same asset to other stock agencies.