Sorry for the slightly late reply. I have researched this a fair bit so can likely give you a good answer.

The whole story is still quite unclear even now. When the wreck of the Titanic was discovered years later it was found to actually be a few miles further away from where the Californian was at the time, so while the Californian was still the closest ship, it wasn't massively close.

Now, on the night of the sinking the Californians wireless operator had been sending ice warnings all day to the Titanic and other ships in the area. At close to midnight the Californians operator once more sent a message to the Titanic warning them that they had stopped for the night due to the risk of ice. The Titanics operator, attempting to work through a backlog of passenger messages replied saying 'shut up, I am busy'. The Californians operator did just that and went to bed. This was pretty standard at the time, there was no requirement to have 24h wireless operators on at the time. Indeed the Carpathias operator was also about to go to sleep when by chance he contacted the Titanic who told him they were sinking.

So the Californian despite being near had no idea the Titanic was initially sinking as they were not receiving any wireless signals. Multiple other ships did respond however such as the Carpathia, Mount Temple, Frankfurt, Caronia, and the Olympic.

Now the rockets are something that is again debatable. At the time there was no standard for either the colour of the rocket, or the firing sequence when used to signal distress. We know the Titanic launched multiple white rockets which were seen by the Californian. However, while not standard, it was generally accepted at the time that red rockets were used to signal distress not white ones, which is likely a reason the Californian did not respond. Knowing the Titanic was a luxury liner, with some of the richest people on earth onboard, on its maiden voyage, it's fairly likely the Californians crew believed it to be some kind of celebration or a show for the passengers as opposed to a distress signal, especially as the Titanic had appeared fine and told them to shut up about an hour earlier.

The differing testimonies are odd, and I can only assume it's because the crew realised they may be getting blamed and were trying to save themselves.

Now there is another theory about a ship even closer to the Titanic, but it's not confirmed. That night, there was allegedly a ship called the Samson which was a schooner that was easily within view of the Titanic. Years later, the crew of the Samson stated they had seen the Titanic and had been within 5 miles of it when it hit the iceberg and saw the distress rockets. However the Samson was a Norwegian ship, which was illegally seal hunting in the area, and also did not recognise the rockets to be distress flares. They may have believed the rockets were flares aiming to identify them, and thinking they had been caught fled back to Iceland.

There is at least some evidence to support this. Officers on the Titanic could see a small ship on the horizon with a single green light which they believed to be close enough to row to, ordering some of the first lifeboats to row there and return for more passengers. Based on the new knowledge of the Titanics differing position compared to Californian, it's possible that the Californian wouldn't have been visible, meaning this mystery ship can't have been the Californian. Furthermore, another ship which came to the Titanics aid, the Mount Temple reported having to take evasive action to avoid colliding with a schooner going the opposite direction as they were rushing to the aid of the Titanic.

Whether or not you believe this is entirely your own decision. I personally believe there may be some truth in it, as the Samson's crew only revealed this years later, and would not gain anything from making it up - indeed it makes them look much worse. The Samson definitely existed and was at least close to the area at the time, having left Iceland four or five days earlier. Furthermore the fact that the Mount Temple reported passing a schooner in close proximity seems odd, as I haven't been able to find any other schooner that was in the area at the time.

Sorry for going off on a huge tangent, but that kind of explains why the Californian didn't respond to the distress signals.

TL;DR: The Californian didn't receive a wireless transmission about the sinking, and believed the rockets were the wrong colour to signal distress.