Just for the record, Papua New Guinea and the Solomon Islands are often shaken by large quakes. It is not uncommon for the quakes to be sizeable - 7+. It *is* unusual to have tsunami warnings, though...but this quake was offshore, and deep. So it's reasonable to have the warning out there.
The series of quakes in OK, Tennessee and thereabouts are the ones that make me wonder...along with the quake in Idaho this morning (a 4.9, iirc). Something seems to be brewing in the center of the country...and that's a concern. The New Madrid fault line is an active one, and these may be foreshocks to a goodish quake in that region.
If you live in that area, I'd strongly suggest that you make sure you have emergency plans ready, including a contact point outside of the region...
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