You will be able to open a new prison after reaching a specific number of rehabilitated prisoners in the previous prisons (eg. “Total Rehabilitated Prisoners: 10000”). However, you should take into account other secondary requirements.
Next to the “OPEN” button, you could find messages like “Requires 7200 reformed Prisoners in Williamson Federal Prison”.
That means that you should reform 10000 prisoners in total, but 7200 of them should be reformed in Williamson’s.
If you only meet one of these requirements (Eg. 8500 reformed prisoners in Williamson and 9500 TOTAL reformed prisoners), you won't be able to unlock the prison. Please double-check both specifications.