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.
ROAD, TRACK, BOWLING, and POOL all fit the category "Things with lanes". Movement is organized into lanes. 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
EVIDENCE / SUSPECT / MOTIVE / ALIBI
EVIDENCE, SUSPECT, MOTIVE, and ALIBI 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
Things that bloom
ROSE / TULIP / ALGAE / FIREWORK
ROSE, TULIP, ALGAE, and FIREWORK all fit the category "Things that bloom". Each can bloom in its own way. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.