If your user was created through the Marketing Cloud, using the reset password link on dtm.adobe.com won't work. You may need to contact support with these details. They can then look through the backend system to see if your user still exists in the DTM system. If it does, they can have the engineering team remove the user. Once this is done, your Marketing Cloud System Admin can remove you from the permissions group and re-add your user. This will create your user in the DTM system again and your account should be automatically linked.
The account was created through the Marketing Cloud and I have never been able to log in to DTM with it. I know that our company uses DTM because of my colleague uses his adobe marketing cloud-id in DTM aswell. And because of that it makes me confused because I should be able to do the same thing.
If your DTM account is enabled for the Marketing Cloud, but the login company for the new invite is a legacy company, the account might be the issue.
First, try accepting the link by logging into the DTM account through DTM (not through the Marketing Cloud). If you receive an error that the password is wrong, use the password reset option.
If the account was created through the Marketing Cloud and was not ever used to log in directly at dtm.adobe.com, a new email address must be used. This is only the case if the account was created via marketing.adobe.com and has never logged in via dtm.adobe.com. This scenario occurs when the invite comes from a legacy company that has not migrated to the Marketing Cloud and the user was created through the Marketing Cloud.