There are volumes of articles and studies out there about when to use complimentary colors and when to go with contrasting colors. By the end of this sentence, there will be another volume written.
Often written within these volumes are chapters devoted to Calls to Actions - AKA CTAs - which will entice a desired action. These written-about desired actions will lead to either sales or leads or whatever is best for your business. Some of it's true. Some of it is written to keep you reading.
Typically written about is how CTAs are most effective when created by contrasting colors. The contrasting color effect makes the CTA stick out. There's a great way to set the contrast. There's a good way to set the CTA. And then there's a way that will make anyone in the viewing area carsick.
Before one starts optimizing the contrast to make their Call-to-Action pop brighter than the others, note the following below:
Just because complementary colors aren't directly used to make a CTA pop doesn't mean they don't serve a valuable purpose. For starters, without some use of complementary colors, there would be nothing for the CTA to contrast against.
Also, most if not all of your brand identity is found within complementary colors. Noting this, all the CTA-focused design won't help if the visitors don't know the reason they're reading the signage.
There's a reason the contrasting colors are also referred to as, clashing. It's because those colors typically don't go together. They're unappealing to the eye. The more those often those unappealing colors are used, you guessed it, the more unappealing the sign becomes.
The same goes for signages for good CTAs. CTAs are those little bit of ugliness that makes the signage stands out, and by doing so, stands out itself. Anymore, and the signage goes from a work of art, and a work that requires that carsick bag to finish.