A couple of things to note.
First off Triumph deviated from the very common tyre pressures of 36/42 PSI to 32/39 PSI on the later bikes. There is a wide range of opinions as to what the most suitable pressures are so you are better off experimenting for yourself to see what suits you best on that one. For instance Bridgestone told me to go to 36/42 when I fitted their tyres regardless of what Triumph said.
From Triumph's user manual
The TPMS warning light will only illuminate red when the front or rear tyre pressure is below the recommended pressure, or no signal is received. It will not illuminate if the tyre is over inflated. So given that the recommended is 32/39 you wouldn't expect to see a warning unless you go below that.
And a reminder, again from Triumph's user manual.
The tyre pressures shown on your instruments indicate the actual tyre pressure at the time of selecting the display. This may differ from the inflation pressure set when the tyres are cold because tyres become warmer during riding, causing the air in the tyre to expand and increase the inflation pressure. The cold inflation pressures specified by Triumph take account of this.