I am sure mirage has nothing to do with this. There are another natural phenomena but haze and/or mirage.[
No, haze had nothing to do with it, Nor did any mysterious mirage effect.
Sound does not bend around the curve of the earth...it travels in a straight line. It is emitted at the moment when the rocket reaches it's maximum altitude. If Beesley saw a flash and heard a boom but no descending stars, then he was seeing that rocket at absolute maximum range from a lifeboat which means it originated about 20 to 23 miles from his position in the lifeboat.
Carpathia fired her first signal when she was 20 miles away from the survivors and arrived there at 4 am. So Beesley was probably reporting the first rocket seen and Stone and Co were reporting the ones fired 45 minutes later when Carpathia was a mere 9 or so miles from him.
However, I believe that Mr. Beesley saw one of the flashes reported by Mr. Gibson.
I doubt he would have heard the sound otherwise.