James Phillips is shown on the 1851 census as a cooper living in Crinow and born in Llanfallteg.................Paul Philipps appears (James is also spelled the same way), he is also noted as a cooper............
Paul Phillip mrd Anne Phillip at Llanfalteg in 1799, however this does not on the face of it appear to equate to the Paul & Phebe of Crinow in 1841 census.
The answer may be in the following ;
Paul Phillips a widower of Crinow mrd Phebe Morris at Robeston Wathen on the 06th Nov 1818.
I note that a James Phillipps a Cooper married Anne Vickers at Crinow on the 02 Nov 1832
The will of William Philipp of Crinow reference SD1758-001 may be related to your research, however he does not mention any Philipps as beneficiaries.
I have been unable to locate any early reference to the Vickers surname in or around the area of your interest which would appear to suggest the family are incomers to the area. I have found the mrge of George Jenkins to Harriet Vickers at Narberth 19 Jul 1831
From my database of Burgess of Pembroke Borough 1678 to 2008 I note ;
Walter Phillips an Auctioneer of Llanvalteg (Llanfalteg) was made burgess 28 Oct 1811 Admin Bk 12 Page 177 Minute Bk page 344
Thomas Phillip a Weaver of Llanvalteg was made burgess 18 May 1795 Admin Bk 7 Page 234 Minute Bk page 357
Johh Phillips a Cooper was made burgess 06 Jan 1766 Admin Bk 4 Page 04 Minute Bk page 11
Thomas Phillips a Cooper of Masgwynne was made burgess 28 Oct 1811 Admin Bk 12 Page 70 Minute book 324
John Phillips a Cooper was made burgess 10 Jan 1774 Admin Bk 4 Page 65 Minute Bk page 45
Rgds
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