Time Line for Albert Albertse Terheunen, the immigrant
1650 June 2 Bpt of daughter Heiltie, New Amsterdam DRC Witnesses: Aert Willemszen and his wife 1651 Aug 13 Bpt of son Albert, New Amsterdam DRC WitnessesWolfert Gerritszen Van Couwenhoven and Grietje Van Nes 1653 Mar3 Bpt of dau Annetje, New Amsterdam DRC Witnesses: Willem Gerritsz, Tryntie Hadders, Tryntie Claes ... 1655 Oct 16 AA and Elbert Elbertse both listed as inhabitants of Amesfoort [Doc. Relative to New York, Vol. 14, p. 336 - Fernow] ...
So, yes Albert may well have been in New Amsterdam 1650-1653/4 - but by 16 October 1655 (before the interesting 1660 map) he was a resident of Amesfoort on Long Island, then New Utrecht, then finally Flatlands/Gravesend where he died in 1685.We don't know WHERE he was between 1638-1650, perhaps working for Stuyvesant.
You will find sources, related to the above, in the endnotes of "Early Dutch Family Ties".