I believe that a separate console should be instantiated on Linux for each TProcess call, by default.
Most, if not all, Unix-like and Unix-derived OS* (as indeed most multi-user systems) can usually run any program/process whether there is a console or not, so whether it's there is up to you (or the user). Which means that running an external process doesn't spawn a terminal session by itself and there are no "standard" facilities to do so.
The common solution (in modern Pascal programs) is to either build your own "teminal" (either an internal or embeded emulator) and link its IO to the process's or run your process as a "command" for the choosen terminal "emulator" (gnome-terminal, xfce4-terminal, etc.) Not really difficult, but neither it's a pice of cake, much less to make it perform seamlessly across several different distros/systems.
* Like e.g. modern Macos, which is based in BSD Unix.