Hugh G. Evelyn-White's hypothesis is that the authors of the non Homeric poems were reasonably aware of Homer's works. This is summarized in the introduction of Hesiod, The Homeric Hymns, and Homerica:
The Trojan Cycle
Six epics with the "Iliad" and the "Odyssey" made up the Trojan Cycle—The "Cyprian Lays", the "Iliad", the "Aethiopis", the "Little Iliad", the "Sack of Troy", the "Returns", the "Odyssey", and the "Telegony".
It has been assumed in the foregoing pages that the poems of the Trojan Cycle are later than the Homeric poems; but, as the opposite view has been held, the reasons for this assumption must now be given. 1) Tradition puts Homer and the Homeric poems proper back in the ages before chronological history began, and at the same time assigns the purely Cyclic poems to definite authors who are dated from the first Olympiad (776 B.C.) downwards. This tradition cannot be purely arbitrary. 2) The Cyclic poets (as we can see from the abstract of Proclus) were careful not to trespass upon ground already occupied by Homer. Thus, when we find that in the "Returns" all the prominent Greek heroes except Odysseus are accounted for, we are forced to believe that the author of this poem knew the "Odyssey" and judged it unnecessary to deal in full with that hero's adventures. In a word, the Cyclic poems are 'written round' the "Iliad" and the "Odyssey". 3) The general structure of these epics is clearly imitative. As M.M. Croiset remark, the abusive Thersites in the "Aethiopis" is clearly copied from the Thersites of the "Iliad"; in the same poem Antilochus, slain by Memnon and avenged by Achilles, is obviously modelled on Patroclus. 4) The geographical knowledge of a poem like the "Returns" is far wider and more precise than that of the "Odyssey". 5) Moreover, in the Cyclic poems epic is clearly degenerating morally—if the expression may be used. The chief greatness of the "Iliad" is in the character of the heroes Achilles and Hector rather than in the actual events which take place: in the Cyclic writers facts rather than character are the objects of interest, and events are so packed together as to leave no space for any exhibition of the play of moral forces. All these reasons justify the view that the poems with which we now have to deal were later than the "Iliad" and "Odyssey", and if we must recognize the possibility of some conventionality in the received dating, we may feel confident that it is at least approximately just.
Source: The Project Gutenberg EBook of Hesiod, The Homeric Hymns, and Homerica, by Homer and Hesiod
I believe this remains the prevalent theory, although the matter is far from settled. And with the evidence as lacking and fragmented as they are, I'm afraid it won't be settled any time soon.