Since boundary changes in 1994 the entire Heathrow area, including Hatton Cross, is now in Hillingdon - the new boundary with Hounslow is the A30. The triple point with Spelthorne is a couple (not "many") miles down the road, just SW of terminal 4. However, when the terminal was built the Spelthorne boundary ran through the middle of both the terminal and the Tube station
Neither the terminals or the station were part of spelthorne or on the border of spelthorne at the time they were built. more than 100 -200 years ago, it (together with feltham, bedfont, and many others) were part of the Spelthorne hundtreth, an administrative section of Middlesex, not a county as such. in 1894 it was part of the Staines Rural Distrct administrative area (still part of Middlesex)
In 1904 until 1965 it was part of the Feltham Urban District (this period includes the airport/Terminal) construction. This is still middlesex.
In 1965 until 1994 it was part of hounslow in London This is the period Hatton Cross Station would have been constructed.
Finally as you have said correctly, in 1994 the area above the A30 was moved to hillingdon.
The modern borough of Spethorne (now in Surrey, not Middlesex) was also created in 1965.
So whilst parts of the airport grounds do border Spetlthorne, the Station was NEVER on the border or in Spelthorne (either the old hundredths abolished in 1894 or the modern borough from 1963)