I had the opportunity today to take a look at the Abridgment of this Sasine. It says, "James Pitullo of Hayfield, Seised, Mar 24, 1787, in Hayfield, comp Wester Hairburnhead, Easter Hairburnhead, Middlemuir of Hairburnhead, Haymains and Blackhill, par West Calder and Mid Calder; part of Towcorse or Tollcross etc, par St Cuthberts; on Ch Resig G S, Feb 3 1787. PR 307.264."
The abridgments usually contain a brief description of the land involved, and tell you who acquired the land, and from whom. This one is unusual in that it does not say from whom James Pitullo acquired it. More to the point, there is no mention of Peter Thomson in the abridgment.
I also discussed this document with a Latin-literate archivist. He agrees with my interpretation of the words 'apud' and 'tanquam'. In other words, that Peter Thomson was probably some sort of intermediary in this transaction, not one of the principals involved in the change of ownership.
There is a later sasine, dated 14 January 1796, in which ownership of the same lands passed to Alexander Young WS. They are described as "the fourth part of Over Williamstone called Wester Hairburnhead, Easter Hairburnhead, Middlemuir of Hairburnhead, fourth part of Over Williamstone called Haymains, and part of the Barony of Marjoribanks called Blackhill, all of which lands are now called Hayfield".
So it looks as if Hayfield may have been a name bestowed relatively recently on part of what was once an estate of four times the size.
I got a bit lost after that because the 1796 sasine refers to one in Kirkcudbright in (I think) 1795. I am at a loss to explain why a sasine in Kirkcudbright is relevant to one in Midlothian, and I couldn't find the Kirkcudbright abridgment anyway as you need a name to locate them and it didn't show up under either Young or Pitullo.
I have been told of two researchers who are skilled at making transcriptions and translations of Latin documents. If you want their names please let me know.