No, the TSA stuff is required for training outside the USA also. However, it is only needed for training for a new license or rating, and it is not needed for recurrent training or revalidating lapsed licenses.
It is required for anybody currently holding a FAR 61.75 (which is what this thread seems to be about) who then wishes to get a full unrestricted FAA certificated because a FAA 61.75 is not considered the 'first issue of a FAA cert'.
Also in addition to what sapperkenno states, remember the requirement for the 3 hours training requirement within 60 days of taking the PTS with a FAA Authorized Instructor as per 61.109(4).
Basically the requirements are documented in FAR 61.107 and 109 for the Private requirements and 61.127 and 129 for Commercial.