The offer was recommended to workers by the unions on Monday morning but they will hold a consultative ballot after a show of hands on the issue was unclear.
One union source said: 'There are 250 men but at least 100 didn't show for the meeting, around 45 voted to accept and around 50 to reject. We can't go to a ballot for industrial action on the basis of one-fifth of the workforce, which is why we will have a consultative ballot to clarify the situation.'
Some Amec staff have pushed for the company to match the 80p an hour and £800 back pay gained by Laing O'Rourke employees on the job in January.
One worker opposed to the offer said: 'All we are asking for is parity with Laing O'Rourke.' The row over bonuses began last year when electricians gained an extra £1 an hour 'productivity bonus' after dropping their demands for a travelling allowance.
Other trades on the contract immediately put in demands for the extra money.
But the union source added: 'This is a fair offer and there doesn't seem to be an appetite for strike action. With Laing O'Rourke, there were 900 men and they had to go on strike for seven days to get the 80p - the original offer was 22p.
'Laing O'Rourke men were also in a more powerful position because the work was critical to the schedule with other trades coming in behind it. With the Amec workers this isn't the case as Amec could just throw more men at the scheme to catch up. The men would just end up costing themselves money in the long run.'
An Amec spokesman said: 'We're disappointed the offer was rejected on a show of hands despite a union recommendation but there were low numbers and high abstentions and we hope a ballot will produce a positive result.'