Do I file "copy 1" of the 1099 misc for four subcontractors in their respective states or do they do it themselves? Will e-file through turbo tax do this or do I mail?

Yes, if the state requires a copy from the payer you will mail it.

States have various laws and requirements and for this reason TurboTax Quick Employer Forms does not offer e-file of these documents to the states.  Many states do not require any document submission for 1099-MISCs from the payer, but some do.  Check the specific state websites for clarification for those states.