Mo, the Auto feature goes WAY back on Roland's.... I can't imagine why any other arranger would do it differently. You also have the Preset button, which, if you prefer to have the new Style's tempo over-ride the old one WITHOUT STOPPING, it can do that. Plus Lock Mode holds the tempo even when you DO stop.
So all three choices are covered.....
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An arranger is just a tool. What matters is what you build with it..!