Mark Williams was crushed after the machine overturned, spilling its load onto the roadway at the Parkway shopping centre job.
The 41-year-old from Oxfordshire was employed by subcontractor Attleys Roofing.
Reading Crown Court heard Williams had complained about a crowded working area forcing him to make many short twists and turns, the day before he died.
Both firms denied four charges brought by the Health and Safety Executive.
These included two counts of failure to conduct a suitable and sufficient risk assessment; one count of failure to ensure health and safety and welfare of an employee at work and one count of exposing others to a risk to health and safety.
The jury found Costain guilty of all four charges and declared Attleys Roofing not guilty on all charges.
Costain will be sentenced on April 23.
In a statement after the verdict, the victim’s family told the BBC: “We’ve sat in court and listened to these companies telling the jury that there was no pressure to get the job done – safety over productivity.”
“It sounds like the perfect site but sadly that is far from the truth. Mark told us it was the worst site he had ever worked on.
“The day before he died, he told Costain in a meeting that ‘someone was going to get killed’.
“Sadly for us, someone did get killed – him.”