There is never any obligation upon an employee to tell his/her employer about matters occurring outside of work unless his/her contract specifically states so (or unless there are professional codes of conduct which impose impose such a requirement).
For example, when I worked on the railways there was a contractual requirement for an employee to report any alcohol-related arrests, convictions or pending court cases. If an employee failed to mention that they'd been arrested for drink-driving, they could be dismissed. But they didn't 't have to report being arrested for theft or violence.
So you need to check your contact.
If your contract (or professional code of conduct doesn't require you to report the caution) but it comes to the attention of your employer anyway, you could only be disciplined or dismissed if it resulted in a 'loss of trust' in your capacity to do your job. (e.g. if you were a teacher and your caution was plastered all over the local press, you could be dismissed because the school governors believed that parents would no longer wish to have you teaching their children).
Chris