There are no issues with the fourth amendment through this. When the first Amber Alerts were sent, the far right had the same reaction because it was Obama.
Could the government track you using your phone? Yes. They had that ability well before any of this system, which is essentially SMS, was developed. You are right to worry. But there are far more insidious tools that were actually developed and deployed well before the 2000s.
Some of the technology has existed before cell phones were even deployed.
Being alert matters…but…this is not the one you should be concerned with.