The reference you found refers to a microfilm although from another NLW reference they also hold the actual document but it only shows the descendants of John Phillips, died ~1629 down to Richard Phillips 2nd bart, died ~1648. Both can be accessed by visiting the library or commissioning photocopies, quite expensive, I believe.
I notice from online trees that the brothers reverted to the patronymic naming system once in Pennsylvania, coming up as Griffith and Samuel ap John. One online tree has their mother, Eleanor dying in Pennsylvania. Is that verified? There are so many Phillips in Pembrokeshire and so few records going back that far I think you have a battle on your hands.
The William Phillips Will is written in Old English I also find it difficult. What I can glean is that seemingly William left no legitimate male heirs, hence the bulk of the estate passed to his brother Morgan after the death of their mother.
I cant read one of the names (attached) says he is a son. Perhaps someone passing by will have a better idea?
WILLIAM PHILLIPS Probate granted 1573
Elizabeth Phillips mother
MORGAN PHILLIPS his brother, inheritance then passed to Morgans male heirs lawfully begotten
Marie Phillips daughter
Elizabeth Phillips daughter
?? son 100 pounds
Harry brother
George Bowen says son?
John and Jane base (illegitimate) children
Niece Elizabeth (looks like Moiriott?)
Other names: Lewis ??; Jenkin Davies; John Johns, my man; Lewis ?? my man; Owen, my Butler. John Wyn owes him 40 pounds
MORGAN PHILLIPS (died bef. 1585) his son and heir was John Phillips who married Ann Perrott, daughter of Sir John Perrott [National Library of Wales, marriage bond dated 11 November 1585]