Praise be to Allah.
There is nothing wrong with using this technique if it is not harmful to the eye, because the basic principle is that things are permissible.
That has no connection to hair extensions, because the technique mentioned is based on dyeing the eyelashes and lifting them, by using some solutions and equipment. It does not involve adding hair to hair, or adding hair from other sources.
But if that is harmful to the eye, then it is haraam, because the Prophet (blessings and peace of Allah be upon him) said: “There should be neither harm nor reciprocating harm.” Narrated by Ahmad (2865), Ibn Maajah (2341); classed as saheeh by al-Albaani in Saheeh Ibn Maajah.
And Allah knows best.