There have been passing mentions of this incident in several accounts without going into specific detail. Obviously, Harold Bride would have known exactly what happened except perhaps the intruder's identity. Since no one else was present and Phillips did not survive, one has to accept Bride's account of the incident, but to what degree I do cannot imagine.
I have often tried to reconstruct the sequence of events but might be off the mark in several ways as this is based solely on accounts of Bride's later reports. It was after Captain Smith had officially released them from duty and so the two wireless operators were by then on their own. It must have been somewhere between 02:10 am and 02:15 am on Monday morning. According to Bride, Phillips was still trying to send out distress calls and was at his desk with his headphones on, while Bride, who had removed hos own headphones, could hear people running about and shouting on the sloping boat deck. By then Bride had put on his own life jacket but the still pre-occupied Phillips had not; reportedly engulfed in admiration at his senior colleagues courage, Bride strapped Phillips own life jacket around the man's shoulders. But if Phillips was seated at his desk at the time still trying to work on the wireless, one assumes that Bride had not fastened Phillips' vest completely.
At around that point Phillips reportedly asked Bride to get their spare money from the inside room and another coat. Bride went in to do so and when he looked out, there was reportedly a stoker who was trying to quietly slip the still pre-occupied Phillips' life jacket off his back (other accounts have that Bride saw Phillips and the stoker scuffling and went to help his colleague). In any case, Bride reportedly said that in a fit of rage at what was going on, he seized "the first thing that he could get hold of" and hit the stoker with it, perhaps several times. At the end of the scuffle the stoker was reportedly lying motionless on the floor of the wireless cabin and in his later 'confessions' Bride reportedly admitted that he might have killed the man. Bride and Phillips cleared out of the wireless room a few moments later, emerging on the port side of the boat deck close to where Lifeboat #4 had been, where Bride reported that he could hear the band still playing ragtime tunes somewhere aft. There was a good deal of noise and confusion with people running in all directions. It was at this point that Phillips and Bride split up, with the former reportedly heading aft towards the rising stern and the latter towards the bow end and eventual survival on top of the overturned Collapsible B lifeboat. As far as I know, no other survivor saw what happened to Jack Phillips afterwards.
Events might have happened exactly as Bride reported them, at at least very close to it. In his reports, Bride appears to have stressed the point that the stoker was a much bigger man than himself but still he, Bride, did not hesitate to attack the intruder. But it seems unlikely to me that even the dedicated Phillips was so distracted that he was allowing the stoker to steal his life jacket and so the more likely scenario is that Phillips and the stoker were already scuffling when Bride went to help. After the man had been silenced, Bride would have known that the intruder would not now be able to survive (irrespective of whether he was still alive or not) and he would have later found out that Phillips did not make it either. That being the case, Bride would have known that there was no real need for him to have reported that incident to anyone at all, since it is highly unlikely that there as any independent witness. The fact that he did report it suggests that it must have been true, or at least very close to the truth.
On the flipside though, the one thing that makes me wonder about Bride's report of that incident is his mention of hearing ragtime music as he and Phillips emerged on the boat deck. Although early reports of the sinking, perhaps with embellishment by media of the time, said that the band were playing right till the very end, modern reconstructions of the final events suggest that the band had stopped playing and dispersed quite some time before the ships final plunge. I doubt very much if they would have had either the ability or inclination to continue to play on the uncomfortably sloping deck while everyone was shouting and trying to save himself or herself. And how could Bride have heard and recognised the tunes amidst all that noise around him?
(On a slightly digressive note, I have always thought that the band and the music that they played that night had a large psychological element. There is no doubt that light music at such stressful times can to some extent help to soothe frayed nerves and so I think that a lot of people were still "hearing" the music in their heads long after the band stopped playing it. This almost certainly would have been the case if the band had played till, say 01:30 and then dispersed; that would explain why so many people, still traumatised by the disaster and unable to think clearly, reported that thy could hear music till the 'very end')