It is the beneficiary of the Member State/Associated Country (the return host institute) who employs the researcher during the whole fellowship duration (36 months maximum). According to the Grant Agreement (Art. 6.2. A), the benficiary is responsible for recruiting the researcher under a contract including social security coverage that also covers the period of secondment to a partner organisation abroad:
...(b) the recruited researcher complies with the following conditions:
(i) be recruited by the beneficiary under an employment contract (or other direct contract with equivalent benefits, including social security coverage) or - if not otherwise possible under national law - under a fixed-amount-fellowship agreement with minimum social security coverage, including for a period of secondment to a 'partner organisation'.
Therefore, the beneficiary will need to ensure that the researcher is covered by social security also for the outgoing phase going abroad. If additional social security costs are incurred during the outgoing phase, these should be covered in principle by the 'mobility allowance'. However, where appropriate due to the high healthcare contributions requested by the country of the outgoing host, the interested parties (beneficiary, host organisation and the fellow) may also agree to use the contribution for the 'management and indirect costs' to cover (in part or full) these additional costs.
For this purpose, the beneficiary can either transfer the required funds to the outgoing host or directly to the fellow. The REA proposes and strongly recommends that this issue is resolved between the partners and the fellow in advance while negotiating their internal arrangements to implement the action.
In addition, regarding the often very high costs of social security coverage in the USA, some Member States have bilateral social security agreements with the USA. It may be worth checking in each specific case if such an arrangement exists as it might remove the need to pay into the health insurance schemes of both countries.