That is incorrect. ICE is able to make arrests for any federal crime they witness while they are performing their duties.
I stole this from Reddit. ICE officers are peace officers. If they have probable cause to believe you committed a federal crime, they can arrest you. If they catch you pirating a copy of Titanic and putting it up on Napster, they can arrest you.
As part of department policy, they would likely get in a fair bit of trouble if they did that. They are funded to perform immigrations and customs enforcement. There is also a very good chance that if you are arrested for stealing James Cameron's royalties, the federal prosecutor will drop the charges because ICE isn't interested in doing any of the follow-up work to secure conviction. But it's not a legal defense that ICE arrested you.
More realistically if ICE is doing some sort of enforcement action and they happen upon you cooking meth as a side hustle from your high school chemistry teaching gig, they are likely going to arrest you and wait for the DEA to come pick you up. That is why Congress gave them that power. But whether it's cooking meth because your son has cerebral palsy, or violating copyright law because you're a huge fan of Leonardo DiCaprio, or blocking the street because you are protesting Trump's heavy handed immigration policies, they are legally able to arrest you.