You ask how our grandfathers would have obtained jobs in these far distant countries. I can only speculate that companies in far-off countries would have advertised in countries with developed mining industries.
You say that according to information you have the Dutch really opened up the mine in 1910, but it appears it had been worked for many centuries before that, which company did your grandfather work for? Given the achievements in the rest of my grandfather's career, I feel he would not have stayed there the time he did (1902-8) unless the Lebong Donok mine was in significant production for a good proportion of it. I can add nothing to the name of the company I gave in my first reply other than that it is a straight translation of the original Dutch in the birth certificate “Mijnbouw Maatschappij Rejang Lebong”.
The name Erdmann & Sielcken means nothing to me.
You ask if I have any pictures of the mine in Sumatra. I have no pictures of any mine. I do have one family group in 1906 in Sumatra on the veranda of what is presumably the residence, which conveys little except something of the style of the house. I also have a picture of the exterior of what is alleged to be his house in the Celebes a few years earlier. It has much in common with the visible detail of the Sumatra house, but sufficient difference to believe it is not the same house.
A cutting about him from the January 1937 number of “The Gold Mining Record” says his prospecting in West Africa was for “Consolidated Gold Fields”. It also refers to Rejang Lebong as “well known”. If you can find a reference library with contemporary numbers of this Journal, you may be able to find out more about Rejang Lebong.
If you are interested in more details of my grandfather’s life, he has an entry in Who Was Who 1941-1950.