Is this a different person? The birth year is way off and she is pretty consistent about it on her US records. She died in Quakertown, Bucks Co, PA in 1954.
U.S., Social Security Applications and Claims Index, 1936-2007
Margaret Watterson Phoenix
Birth Date: 13 Jun 1881
Birth Place: Margrafelt C, United Kingdom
Father: James Watterson
Mother: Margret Hurl
SSN: 183077732
Notes: Dec 1936: Name listed as MARGARET WATTERSON PHOENIX
[the number was issued in Pennsylvania]
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The birth year matches on this lady, but the nationality and destination do not. Just in case it is her:
On the SS Gallia, arriving September 30, 1892, at New York from Liverpool
Kate Proctor, 28, cook,
Margaret J Waterson, 19, spinster,
Anna Waterson, 20, spinster,
All English citizens, all headed to Ohio, all traveling in 2nd cabin, all left from Liverpool.
Kate Proctor says she intends a protracted sojourn in the US
The Watersons say they intend to be transient.
On the other hand, there were Irish citizens on the next page, so these 3 most likely were from England, not just English citizens because they were ruled from England.
https://heritage.statueofliberty.org/passenger-details/czoxMjoiNjA0MzQzMDUyMTI0Ijs=/czo4OiJtYW5pZmVzdCI7-----------
And I found this man while searching. I assume you have him, but just in case:
U.S., Social Security Applications and Claims Index, 1936-2007
Name: Adam Watterson
Gender: Male
Race: White
Birth Date: 6 May 1885
Birth Place: County Dariy, Republic of Ireland [their transcription, not mine]
Father: James Watterson
Mother: Margeret Hurl
SSN: 161122742
