But it doesn't. When you click on my head on Medium, I don't expect you to land on my home page , or my company page, or any other page that is mine on the internet. As far as Medium and readers are concerned, my Medium profile is your destination (https://medium.com/@kirillzubovsky). On there you see all my posts and all the social information that I provided, and you can further explore the service and/or my links if you choose to.
The equivalent of a Tumblr logo on Medium would be their "M" logo. When you click that, you end up on their front page, and not on my profile, which is what you should expect.
You are partially correct, this implies that the user understands the basic behavior of the web and expects my photo to lead to one place and "M" to another.