13 seconds with 3 time outs, is much different than 13 seconds with no time outs. Chiefs could still use the whole field, so the Bills had to defend the entire field. With no timeouts, the only option the Chiefs would have had was to throw to the sidelines.
Time management is definitely something Reid has improved on on over the past years. Which allowed the Chiefs to manage the clock for the winning drive. Buffalo used their timeouts too early.