TSA clearance and visas are two different things handled by different branches of the government. (TSA - US Department of Homeland Security, visas - US Department of State)
TSA clearence is needed for initial licence (PPL), IR and ME. Seperate application is needed for each course of study even if they are to be undertaken at the same time (See
https://www.flightschoolcandidates.gov/ for more details)
M-1 visa is needed for any vocational course of study, including PPL, CPL. ATPL, CFI, etc. (See
http://www.unitedstatesvisas.gov/ for more info).
As has been said, neither TSA nor M-1 visa are needed for hours building, BFR, etc. If in doubt contact your local US Embassy (theres a list at
http://www.usembassy.gov/)