The Construction Workers Compensation Scheme (TCWCS) is urging sector staff to get in touch and find out if they are entitled to a payout - but the GMB union has described the project as "grossly inadequate".
The scheme has been set up by the firms to compensate workers whose details were held on a database that effectively blacklisted them and prevented them from gaining employment, especially those who were known union or health and safety activists.
It offers workers a "fast-track" route to compensation - meaning that if their name is on the list they will be guaranteed a payout of between £4,000 and £20,000 within two weeks. There is also a full review process available, which takes longer but could attract sums of up to £100,000.
However, GMB said the total amount estimated for the scheme fell woefully short for major firms with pre-tax profits of £1.04 billion.
The union's Scotland secretary Harry Donaldson said: "The total compensation which they offered in June is estimated to be between £15 million and £20m. That is less than £3m per company.
"This is grossly inadequate to deal with the devastating damage inflicted on people in their working lives and the colossal invasion of their privacy. The companies should get serious and make proper restitution and close the book on this shameful chapter.
"The eight companies between them have a turnover of over £34bn and pre-tax profits of £1.04bn. The employers have to own up, clean up and pay up."
The union is pursuing legal action through the courts for 122 of its members in an attempt to secure a better payout.
It has also called for the firms involved - including Balfour Beatty, Carillion, Costain, Kier, Laing O'Rourke, Sir Robert McAlpine, Skanska UK and VINCI PLC - to be banned from tendering from public contracts until restitution is made.
A spokeswoman for TCWCS said the scheme was there as an alternative for those who did not want to go through a lengthy court procedure, with claimants on the fast-track route only required to provide proof of their identity to receive a guaranteed payout if their name is on the list.
She added that the project -which was created following an eight-month consultation with the unions - did not require any proof of loss of earnings.
The spokeswoman said: "We are encouraging anyone in Scotland who worked in construction in the years leading up to and including 2009 to contact the TCWCS freephone helpline or look at the website for further information. We are keen to find as many people as possible who are eligible for compensation, so do get in touch.
"Or if you know someone else who worked in construction, please encourage them to pick up the phone to us or log onto www.tcwcs.co.uk to find out whether they are eligible for compensation.
"Enquiries to the scheme are handled quickly and, if you are eligible, joining the scheme is completely free of charge."