Should I inform my potential advisor that my paper got rejected?
I don't think that being rejected by a top tier journal of your field should reduce your chances to get the PhD position in any way. Your potential advisor most likely knows this all too well. This is part of the scientific professional life. I would assume that s/he can judge the work you did regardless of his field of expertise our whether it got accepted or not. But if it was well written, presented in a clear and structured way, he or she will appreciate that because it is such an important skill. 

You don't need to mention it yourself if you feel uncomfortable about that. However if you want, you can say that you got rejected by X, but think that with the feedback you got you can really improve the manuscript and will try to publish it elsewhere. This will show your motivation. Most likely your advisor will be happy about that.