The biggest question that appears to have escaped the Irish idiot is if it is a mobile phone it must be some kind of "time phone" who is she going to talk to with no cell towers or infrastructure around? Hence it's not a phone at all.
Also his theory would suggest that there are time machines in existence right now or in the near future, and whilst I cannot 100% disprove this I personally believe that Human technology has not reached the point at which anyone could time travel yet, not for a good many decades at least or at least until the singularity.
Further to that point, if it were a time traveler why have we not seen more of this in other films or photos? Why go through the hassle of wearing period clothing and then talk on a mobile phone? The fact that the person is old also casts doubt on the situation, if there were a singular time traveler (as we have not seen more) then surely he didn't simultaneously create a time machine and a completely unnecessary "time phone" in his basement.
His claims of showing it to 100 people who could not offer one explanation as to what it could be only further strengthens the stereotype of stupid Irish people. There are many more plausible theories to garner from that section of film, the least likely and least logical being that he/she is a time traveler. I bet his backup theory is that it's a ghost.