There's two aspects to that: Licensing and academic ethics.
Regarding licensing, you write that you have a license that covers personal and commercial use. Probably commercial use will include academic (i.e., professional) use, but make sure that your license permits you to reuse these elements in a publication. For a poster I don't think it will be a problem. For a research paper, you typically need to transfer copyright to the publisher, which you can't for these elements. So that will need special consideration.
Regarding academic ethics, the way to answer this question is to think about the scientific contribution that is being made with these elements. Does the creator of these elements contribute in any way to the scientific content of your publication? If yes, you should give an attribution, if not, an attribution is not required.
It's not clear to me how much science did go into constructing these elements, but think of the following extreme case: When writing a paper, you obviously use graphic elements, which are the font of the letters, to convey your message. But typically, you don't attribute the creator of the font, because there's no contribution to the scientific content. It's really just the medium you are using to communicate your results, and you don't need to attribute that.