The full solution is below, with a short explanation for each group. To avoid spoilers, play the puzzle or open the hints page before reading the answer panels.
PEPPER, WASABI, GINGER, and CHILI all fit the category "Spicy things". They can wake up your taste buds. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Mystery story clues
MOTIVE / ALIBI / EVIDENCE / SUSPECT
MOTIVE, ALIBI, EVIDENCE, and SUSPECT all fit the category "Mystery story clues". A detective asks about these. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Things that ring
CASHIER / ALARM / BELL / PHONE
CASHIER, ALARM, BELL, and PHONE all fit the category "Things that ring". Each can make a ringing sound. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Fast things
FALCON / ARROW / COMET / SPRINTER
FALCON, ARROW, COMET, and SPRINTER all fit the category "Fast things". Speed is the common thread. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.