Hola Joseph

I checked the writing challenge and what is said about the weather. In general, if you are referring to the weather getting better, you can definitely use "el tiempo está mejor", but in this challenge, it is referring to what the weather is like in general in spring:

Con la llegada de la primavera

vamos a organizar muchas excursiones

ya que el tiempo es mejor

y los días son más largos.

It's not really saying that "now" that it is spring, the weather "got" better; it is describing the weather everytime spring comes, a general description. 

I hope this clarified it.

Saludos

Inma