Here is an example tree, and a couple of figures drawn from it. It is usually not the whole tree that is misrooted or "inside out", but just one clade within the tree. I am attaching here a tree that appears to have an example of the issue. The HIV-1 M group subtype B epidemic began in Haiti and then there were hundreds of exports of the virus from Haiti to other parts of the world. The sub-epidemic of subtype B introduction into South Korea happened in 1989 or 1990 and most likely did not come straight out of Haiti. Subtype B spread into Trinidad and Tobago much earlier than 1990, but there was not much sampling and sequencing of viruses there until more recently, so there is a bit of a bias there for isolates in the post 2005 time period in comparison to USA/Europe where we have a lot of sequences from viruses sampled in the 1984 - 2000 time period.
In this tree, we might get the impression that the viruses from South Korea and Trinidad/Tobago originate near the "root" of the subtype B clade which I have labeled as Root 1 in red. But it is far more likely, given all that we know of the epidemiology of HIV-1 subtype B, that the true root of the B clade is close the the green node I have labeled as "root 2".
When the tree is drawn as a radial tree like this, it gives us a bit of a different impression that when it is drawn as a cladogram. And in either tree view, if we measure distances from tips to "root 1" we get different values than if we measure distances from tips to "root 2".
The chat software here does not allow me to upload the treefile or alignment, but I can send it to anyone who wants it.