I'm only lightly familiar with the "Navy-way" of bridge/navigation watches.
Can anybody here outline how many are on watch at a time and what they're supposed to be doing?
OOD - Officer of the Deck. Responsible for the safety, navigation, and operation of the ship during his watch. In that role, he answers only to the CO or, in tactical situations, to the Tactical Action Officer (TAO), and even then, only in the maneuver or fighting of the ship. He should know where every surface and sub-surface contact within sensor range is, along with the status of weapons, the engine room, the plan of the day (POD), etc.
JOOD - Junior Officer of the Deck. Also called the Conning Officer. Responsible for the safe steering of the vessel. He gives the rudder and engine commands. Reports to the OOD. He should know where every surface and sub-surface contact within sensor range is.
CICWO - Combat Information Center Watch Officer. Responsible for ensuring that the CIC watch is doing their job, part of which is safe navigation and maneuvering of the ship, and another part of which is tracking all surface, sub-surface, and air contacts.
Surface Supervisor - Enlisted guy in CIC whose sole job is to detect and track all surface contacts in sensor range.
Lookouts - At least three of them (Port, Starboard, and Aft). They would have been reporting the proximity of any vessel within visual range. I'd say this tanker was within visual range.
TAO - Tactical Action Officer. Assuming one was on watch (normal during operations, but not necessarily during peacetime transits), he would know where every contact in sensor range is, as well as any coming in from other ships and aircraft over the data link.
If this happened during an UNREP (Underway Replenshment), then the Captain was or should have been on the bridge. The XO may or may not have been. I remember the XO normally being up forward or back aft at one of the UNREP stations, with the Ops officer being at the other.
So, in short, the OOD, JOOD, CICWO, SS, and CO are probably all toast. Others will depend upon the logs showing recommendations and warnings. In fact, if the logs show, for example, that the CICWO, OOD, and JOOD all recommended appropriate maneuvers to avoid collision, but the CO ignored them, they will stand a good chance of saving their skins.
No matter what happens or what the logs show, however, the CO's career is over. The tanker could have been coming to ram the ship on purpose, and the CO would still be responsible.