Ariana chose Jimmy because she knew her butler could do it. Not only strong, but Jimmy is also an expert in dealing with many problems. Ariana knew she could leave Alison's territory in good hands if she gave Jimmy that responsibility.
In the end, Jimmy is forced to relent through Ariana's strict orders. No matter how hard Jimmy tried to make his request, Ariana pointed out that it was Jimmy's job to protect Alison's territory while Ariana was away. Jimmy also realized, in the end, that no one could take that position but himself. Jimmy finally relented, even though he repeatedly reminded Ariana of the extra security she had to carry with her along the way.
"Jimmy," Ariana called again. The girl thought for a moment before she made up her mind.