It's important to be in the correct gear at all times to have optimum throttle control & good response to change lines or speed quickly. Good mid-range torque, typical of Triumphs, really helps here
So changing down quickly, blipping the throttle to match rpm & road speed is what's needed when breaking. Heavy braking just means the technique has to be accomplished a bit faster & with more downshifts. Typical scenario, as other posts have mentioned, is approaching a bend at speed.
With a bit of practice it's possible to be pulling hard with four fingers on the brake lever & rock the throttle back with the palm of the hand as required. Some modern bikes (& race bikes) have 'two finger' brakes making throttle control whilst braking easier. No such luxury on the classic triples & twins...
Controlling the throttle with just the palm (thumb placement can sometimes help too) in this way is handy in another situation. That is when approaching a 'hazard' - say, for example a dozy looking cager waiting to pull out - you can 'cover' the front brake lever whilst keeping the throttle steady. Covering the front brake this way (& clutch as well of course) can save vital time (distance!) if an emergency stop becomes neccesary. (You're already covering the rear brake, as you should be anyway, right

)
A good practice techique is to go up & down say 3 gears whilst keeping a constant road speed (most bikes have close enough ratios for this) & four fingers covering the front brake. Keeps the skills sharp to be prepared (& in the right gear) for any situation.