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.
BELL, CASHIER, ALARM, 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
Coffee shop orders
AMERICANO / MOCHA / LATTE / CORTADO
AMERICANO, MOCHA, LATTE, and CORTADO all fit the category "Coffee shop orders". You can hear these at a counter before 9 a.m. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Spicy things
PEPPER / WASABI / CHILI / GINGER
PEPPER, WASABI, CHILI, and GINGER 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
Musical directions
FORTE / ALLEGRO / PIANO / ADAGIO
FORTE, ALLEGRO, PIANO, and ADAGIO all fit the category "Musical directions". A score might tell a player these. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.