If you do something demonstratively, you do it in a way that shows you care — openly, where it can be seen. You might hug someone demonstratively, or hold a hand demonstratively, so the feeling is not a secret. The adverb almost always sits next to an action: hug, greet, kiss, hold. It can sound a little stiff in speech; people more often just show it, or say “in a really warm way.” The idea is the same as demonstrative, only now it describes how the act is done, not the person.