Private entities are beyond ambit of RTI Act and there is no such designation of Public Information officers in private organisation.
If the contractor is not maintaining such register properly, first you have to make complaint to Inspector of labour and ask him to collect the muster roll copies for verification. Once contractor submits that to Labour inspector you can obtain the same from Labour dept., which is within ambit of RTI Act.
Under RTI Any Citizen can collect such information that is already available in custody and control of Public Authority in material form. Please read this single sentence to understand basics of RTI.