There are a number of problems with this. One is that Tesla didn't have a good grasp of electromagnetic radiation, nor did he accept quantum theory, so he would have had serious problems with the mechanisms required to make a mobile phone work.
More to the point, though, Tesla's handwaving remark was in a long tradition of broad predictive comments which certainly show that an individual is open minded, but do not necessarily indicate that they are inventing something ahead of its time.
For instance, I dearly love the thirteenth century friar Roger Bacon - so much so that I've even written a book about him. But no one sensible would suggest that Bacon understood television or aircraft. If, however, I use the 'Tesla foresaw X' approach, he seemed to predict both. In one short burst in a letter to an acquaintance, for instance, he listed self-powered ships, the horseless carriage, the flying machine, something that sounds like a pulley system, and a diving suit or diving bell, most of which would not become practical for another 600 years.
Elsewhere he wrote:
We may read the smallest letters at an incredible distance, we may see objects however small they may be, and we may cause the stars to appear wherever we wish. So, it is thought, Julius Caesar spied into Gaul from the seashore and by optical devices learned the position and arrangement of the camps and towns of Brittany.Such devices are very unlikely to have existed in Bacon's day (let alone Julius Caesar's) - the first microscopes and telescopes would not come along for about 300 years. And to make some of Bacon's claims true would need TV rather than a simple optical system.
Admittedly it's possible that Bacon achieved something like a crude telescope and/or microscope by messing about with lenses - but certainly nothing capable of what he described, nor would he understand how to do it. Bacon was not 'describing a telescope' any more than Tesla was 'describing a cell phone.' Tesla was speculating, given the knowledge of the time, as many others did, what was possible in principle. And that's a very different thing. Nikola Tesla was one of the greatest electrical engineers ever, but this kind of myth building doesn't do science any favours.