This is apparently a big controversy, but I was under the impression that the US and Taiwan were allies - there's a lot of trade, certainly, I have many items that are "Made in Taiwan". Surely there must have been trade agreements, tariffs, etc., at minimum?
The United States and Taiwan do maintain unofficial relations since the US recognised PRC as China in 1979.
It's widely reported that Donald Trump's phone call with Tsai Ing-wen is the first known call between a President or President-elect of the US and the President of Taiwan since 1979. Government officials surely have communicated.
However, the fact is that we all know the call occurred, since Trump twittered it on Twitter and publicly acknowledged it. Had he not shared it, we might not have known that this had even occurred. So it might be that past Presidents just contacted the Taiwanese leader silently.
You are perfectly right that there are agreements between the US and Taiwan. Jimmy Carter signed into law the Taiwan Relations Act, which established unofficial relations. It opened the American Institute in Taiwan (acts as an embassy) to facilitate interaction.
In 2015, the Obama administration sold $1.83 billion of frigates to Taiwan under the Taiwan Relations Act Affirmation and Naval Vessel Transfer Act of 2014 passed by Congress.
The controversy created by Trump is that he publicly acknowledge that the President of Taiwan called him to congratulate him. The fact that China doesn't recognise Taiwan means that China doesn't mention the Taiwanese leader as President, so as not to imply it as a country. Rather, it refers to him as Leader of Taiwan, which reflects China's stance on Taiwan.