Hi!
のんびりしています in this sentence doesn't indicate a progressive action. The ~ている form can also be used to indicate a particular state or condition.
Examples:
1. 瘦せる "to get thin" → 瘦せている "to be thin"
2. 乗る "ride or take (a bus, a car, etc.)" → 乗っている "be in a bus, car, etc."
3. 眼鏡をかける "to wear glasses" → 眼鏡をかけている "be wearing glasses"
Therefore, regarding のんびりしています in your sentence, it means "to be more easygoing"
You can't use します in ジョンはデレクよりのんびりします。to express the same statement.
I believe that ツンデレ colloquially indicates a chill, cold or aloof personality.
Hope that helps.