It starts with minimum wage laws changing so that waiters and bartenders are not exempt from normal minimum wages. Start there.
There was some talk about if people would stop tipping. Nope, people still tip!
Most places in the US require businesses to "make up" the delta between minimum wage and what the employee receives through wage+tips. Seattle just codified this more clearly by having a "minimum wage" and a separate (higher) "minimum compensation". So while wait staff have a minimum compensation of $15/hr, that number is inclusive of tips they receive. Their minimum wage (what the business has to pay regardless of tip) is lower at $12/hr.
People may have considered no longer tipping because of the publicity behind the new-to-them-but-not-actually-new concept of minimum compensation but it's effectively the same system at a higher number.