12" across (assuming you mean from arm tip to arm tip as the diameter of a circle with the body in the center) does not sound like an adult vulgaris. Did you notice any particular markings on the animal like spots that showed all the time or a colored circle just below the eyes? A lot of activity just before brooding is common to most species, even the nocturnals. Do you have any photos of the female?
How large are the eggs? Look at them and then give a size example that is common rather than (or in addition to) trying to estimate mm (pea, eraser, round pushpin head, etc ...). Extracting one and photographing it next to a ruler or coin would also be helpful.
Vulgaris is a small egg species and hatchlings would be very, very small (rice size) with only a few chromataphores and arms and mantle about the same size at hatching. A larger egged species would have eggs about the size of an eraser or the barrel type push pin, usually take longer to hatch and look much like minature adults. There is almost no chance of raising the small egg (planktonic) animals in a home aquarium and even the larger institutions have only had minimal success with a few species. Within TONMO three of the larger egg species (bimaculoides, mercatoris, briareus) have succeeded in surviving but only the bimaculoides was successful with a large number of hatchlings maturing to adults.
There has been minimal success with trying to viably hatch (as in long term survival) eggs without the mother. An article I recently read trying to determine my best shot at rearing O. briareus indicated that the eggs needed regular stimulation (movement) to survive or the outer eggs would fatally inhibit the growth of the inner ones. Also, watch the urchin as it might find the eggs an attractive meal (but could not gobble them up overnight I don't think). With the mother dieing so soon after laying the eggs, there is a good chance that they are not fertile. Watch for small black dots to appear. The infertile eggs I have had did not last more than two weeks before they rotted away.
I have a progressive journal on Kooah and her eggs that might offer some ideas on what to watch for but small egg species (excepting the Giant Pacific Octopus) tend to hatch much more quickly, some in as little as 10 days, than the large egg variety.