"Simple caution" sounds like a warning, not being in violation. I don't know your jurisdiction but most police departments enter warnings in their "wants and warrants" data base. If another officer runs you in the data base, he/she will know you have already been warned and move on to step two. You can call the department that issued it and verify that is correct. If it is, the questions that affect visas are about convictions (you go to court), not warnings.
In the UK, a "simple caution" is not just a warning, it is a record of an admission of guilt (formerly known as a "formal caution") that, since in a change in the law in 2009, is stored on the Police National Computer for a period of 99 years. However, a caution is not a conviction, so if your application only asks about convictions, you can truthfully say you have none.