// Article 31 of the Refugee Convention 1967 concerns the responsibilities of Asylum seekers "surrendering without delay to the authorities" //
Article 31 is concerned more with the responsiblity of the contracting state rather than the responsibility of the refugee. The phrase they use is "presenting themselves" rather than surrendering.
// Article 31
refugees unlawfully in the country of refugee
1. The Contracting States shall not impose penalties, on account of their illegal entry or presence, on refugees who, coming directly from a territory where their life or freedom was threatened in the sense of article 1, enter or are present in their territory without authorization, provided they present themselves without delay to the authorities and show good cause for their illegal entry or presence.
2. TheContractingStatesshallnotapplytothemovementsofsuchrefu- gees restrictions other than those which are necessary and such restrictions shall only be applied until their status in the country is regularized or they obtain admission into another country. The Contracting States shall allow such refugees a reasonable period and all the necessary facilities to obtain admission into another country. //
http://www.unhcr.org/protect/PROTECTION/3b66c2aa10.pdf
There is nothing in the 1967 Convention about the first state they arrive at must take them.