Chances of getting sick from reusing utensils after checking chicken doneness
The chances are very low that anyone would get sick from that because the chicken was probably already safe when you first checked it. Although the recommendation is to cook until the chicken is 160F, anything above 140F will start to kill salmonella pretty quickly, with 4 minutes at 145F being enough to kill it off. A handy table from this page gives good info:

Min Internal Temp °F  6.5 log lethality   7.0 log lethality
    130°F                  112 min             121 min
    135°F                  36 min              37 min
    140°F                  12 min              12 min
    145°F                  4 min               4 min
    150°F                  67 seconds          72 seconds


6.5 log means 99.99997% is killed 7.0 log means 99.99999999% is killed. At 160F the 7.0 log time is 4 seconds, which is why there's a recommendation to cook to that temperature.
From your description it sounds like your chicken was close to being done but not quite done, so you erred on the side of caution and cooked longer, it was probably above 150F, so the salmonella should have been dead.
But, just because you got away with it this time doesn't mean you should make a habit of it! As someone who has experienced the great fun that salmonella poisoning is I would encourage people to wash their utensils if there's ever any possibility that they've come into contact with undercooked chicken (or seafood for that matter, not salmonella but just as bad or worse).