I believe the specific legacy descriptions have information on whether a given legacy is available for mages walking a different path than the legacy's parent. It is possible in some cases to do so:
Legacies are learned by way of a mage’s Path, although some orders can
teach certain Path Legacies to members not of that Path.
– M:tAw p.344
For example, the "Subtle Ones" legacy is available for mages who are Obrimos and/or are members of the Guardians of the Veil, whereas "The Orphans of Proteus" are exclusively of the Thyrsus path (besides the specification of their "Parent Path", their "Organization" entry also points this out: "All Orphans are Thyrsus (...)".
Edit: As for your example, I think Transhuman Engineers have to be Obrimos, since that's what their Parent Path defines (unlike, for example, The Stone Scribes from the same book - Legacies: The Sublime -, who have a "Parent Path or Order" definition with "Moros or Mysterium" specified.)