Aren’t all police agencies required to check on your warrants and report those to whatever jurisdiction they are from?

Yes

But as far as ICE, are you saying the Houston police are required to report people to ICE?

No. In fact, cities like Houston and Austin try to not volunteer information that they are not required to by law. If you read the article you’ll see that the lady that called the police has an active deportation warrant, which is why the police officer was obligated to notify ICE and also why the police officer told her to not show up.