This pre-trial and trial detention set-up works well for the US. With the case of Marine Daniel Smith, he was detained inside the US Embassy for around three years, until it was proven that the charges were totally fabricated. It was a logistical nightmare for the Embassy.
In this case, the Filipinos are glad to have him, and the US is glad that the Filipinos have to deal with his incarceration during the trial.
I presume the US Marines guarding him are Marine brig guards borrowed from the Peleliu.
Where he serves his time, if convicted, will be another question...to be dealt with later.