Step 1 areas of trees close to but not included in the construction fence off, no go to anyone
Step 2 areas inside the construction zone....where the foundations for the deck are going spread a thick layer of mulch across the entire area to protect the soil and roots from compactin during construction
Step 3 ensure your builder knows how much importance you are placing on the trees....you're the boss you run the site according to your site rules...tree protection 1st, builders convenience last
Step 4 select subfloor bearers with the largest span capacity...ie strongest beams you can afford this way you'll need less posts less foundations less impact
Step 5 work with the person designing the sub floor pattern to avoid as much as possible the visible buttress roots, and to give you some flexibility in post location..bigger span distances allow you to reduce the post numbers inside the deck.......from something like this
To something like this
Step 6 when digging for the foundations if you can use a water blaster (very long hose) to open up the post holes, this way you can find any roots in the holes and where possible adjust locations accordingly, those you do find that can't be avoided clean cut...don't tear.
Step 7 ensure no soil contamination outside of foundation holes..no wash down inside root zones, no storage of building materials inside root zones, no heavy plant machinery in there either..mostly manual labour.
Step 8 at the end of the job depending on your climate of course! Water the trees with a dilute solution of seaweed extract and fish emulsion 1:100, a dilute solution of molasses will really help promote root growth and health too.