This seems to only be getting coverage in the Turkish press, but a few people were kind enough to send me links to stories and information.
To start with, I was incorrect in my first version in saying that the tomb was securely linked to Hecatomnus by an inscription, as one account stated. Apparently the tomb had been looted, and there were no inscriptions.
Hecatomnus was appointed Satrap of Caria, and had the distinction of being the first non-Persian appointed to this office. He was a native Carian whose family can possibly be traced back to circa 500 BC, and whose ancestors sometime in the 5th century seem to have become priest-kings of Zeus Carius at Mylasa, the pan-Carian cult centre.
The sarcophagus in a tomb chamber was found some 12 m down, under the site believed to have been the location of the temple of Zeus at Mylasa (modern Milas). Scholars also believe that this was the location of the 'royal' palace of the Dynasty. When I saw a detail of the reclining bearded figure carved on the sarcophagus, I first thought they had used a photograph of a marble panel from Iasos to illustrate the story; they are both linked to the Hecatomnid Dynasty, and both produced in that Archaising style the Dynasty favoured.
Though the tomb and the sarcophagus had been looted. This is clear as the lid of the sarcophagus was smashed by the tomb robbers - which is a pity as bones would have provided us with fascinating insight into the man - but it is still a remarkable find, and one of the most exciting of recent decades. The sarcophagus depicts the deceased reclining in state in the centre of the long 'front', and depicts different scenes on the other sides; the short ends are carved with mourning women not unlike the Mourning Women Sarcophagus (from Sidon, now in Istanbul). Statues of mourning Heliades between the columns on the interior of the Belevi Tomb are now lost, but attested there by an inscription; and my reconstruction of the Mausoleum at Halicarnassus would include a row of mourning women around the high base.
It's an important person's tomb, and dates from the first half of the 4th century BC. It can't be Mausolus since numerous sources attest clearly that he was buried in his own eponymous Mausoleum in Halicarnassus, but it must presumably be an earlier Hecatomnid since they were in power in Milas at the time.
I don't know what the evidence for the c. 390 BC date of the tomb is, but if we're to place it then, I would suggest that Hecatomnus' father Hyssaldomus - the priest-king of the Carians, although probably not Satrap of Caria - must also be considered as a probable occupant. If the dating is purely stylistic, then the sarcophagus could be from the 370s BC and more likely to have contained Hecatomnus himself. The portrait on the deceased, like the Mausoleum portrait of Mausolus, is not overly idealised, and an attempt at portraiture.
The tomb, since it was beneath the temple, pre-dated it; the columns of the current temple look Hadrianic to me (more were in the garden of the local museum, under a bush last time I visited). The temple is identified as one of Zeus by an inscription, although this is probably one of the three temples of Zeus in the city rather than the temple of Zeus Carius (which is believed to have been on a ridge on the edge of the city).
The woman seated to the right of the reclining Hecatomnus would be his wife (whose name is not known). She is wearing a tiara, which confirms that she is royal, so almost certainly a Hecatomnid.
The two youths would be his younger sons, and the veiled woman at the right one of his mourning daughters; since she is the counterpart to Mausolus, she was presumably his sister-wife Artemisia.
We know that Hecatomnus had two daughters - Artemisia II and Ada - but the two smaller children depicted on the front seem to be boys. This is interesting, as it would suggest Ada is one of the mourning women on the side of the sarcophagus, and that there were two more sons who either died in childhood or were not deemed worthy to be recorded by history.
The back of the sarcophagus seems to have shown Hecatomnus hunting or fighting, with one arm raised holding an inserted (and now looted) bronze spear. This recalls the slightly later Alexander Sarcophagus (also from Sidon and now in Istanbul).
We'll that's my quick analysis based on the photos. On a personal note, if I ever come across the people who looted this tomb, I will string them up and torture them.
For more photos, see my original post here.