Quite an unusual situation here.
Firstly I am not sure you have the power to INSTRUCT them to start earlier than the starting date (or even why you would want to), but by agreement obviously they can. If they are to start four weeks earlier and their whole programme can just shuffle forward by four weeks (which is not necessarily the case) then planned Completion comes forward by four weeks but Completion Date will not move, hence yes creating four weeks terminal float which the Subcontractor then owns. However, they can't price that four week period as "prelims" - it will just give them an extra four week period where they could overrun without incurring delay damages. Any CE is meant to allow them additional cost they are incurring - and if planned Completion is coming forward by four weeks by starting four weeks earlier they are NOT incurring an extra four weeks prelims.
As for whether a Subcontractor can/should price the terminal float period at tender stage - it is within their gift to choose to or not. However, if they want to make sure they win the tender they would be ill advised to price for that period. In your example they had two weeks terminal float at tender stage. If they are saying that they can do the works in 28 weeks(say) and the Completion Date you have stated is at week 30, they only need price 28 weeks prelims within their bid. If ever you gave them a CE that moved planned Completion from week 28 to week 30, they would be entitled to claim two weeks worth of prelims. If they did price it at 30 weeks then they are just lucky they still won the bid.
Firstly I am not sure you have the power to INSTRUCT them to start earlier than the starting date (or even why you would want to), but by agreement obviously they can. If they are to start four weeks earlier and their whole programme can just shuffle forward by four weeks (which is not necessarily the case) then planned Completion comes forward by four weeks but Completion Date will not move, hence yes creating four weeks terminal float which the Subcontractor then owns. However, they can't price that four week period as "prelims" - it will just give them an extra four week period where they could overrun without incurring delay damages. Any CE is meant to allow them additional cost they are incurring - and if planned Completion is coming forward by four weeks by starting four weeks earlier they are NOT incurring an extra four weeks prelims.
As for whether a Subcontractor can/should price the terminal float period at tender stage - it is within their gift to choose to or not. However, if they want to make sure they win the tender they would be ill advised to price for that period. In your example they had two weeks terminal float at tender stage. If they are saying that they can do the works in 28 weeks(say) and the Completion Date you have stated is at week 30, they only need price 28 weeks prelims within their bid. If ever you gave them a CE that moved planned Completion from week 28 to week 30, they would be entitled to claim two weeks worth of prelims. If they did price it at 30 weeks then they are just lucky they still won the bid.