This is confusing me what you're saying. Once a player is 20 years old, training slows down. Once he reaches his cap, it will either train really slowly, or just stop. DMI is how well your player trained the past week. If its over his regular, he was trained. Game shape will make this increase too, since he got a good amount of minutes.
So, at what point does my player stop training normally and start training really slow? For instance, if a player has the potential of a starter, does he reach his cap at "proficient" or is that determined by his DMI? Is this explained anywhere (at least somewhere in the forums) or do I simply have to observe his DMI?
The soft cap can not be determined by a level in one skill. It is quite close to the system of the salary. If I remember correctly, a potential of starter hits his cap at maybe 15k (this I am not sure about, could be 10 or 20 but anyhow..), and the DMI does not matter whatsoever. You can find the soft cap vs salary tables here in the forums, they are mentioned every now and then, I don't have the time now to search.