A serious actor would have a cover phone that was their main phone and had truly been used for everything they did, other than eee-ville, for months or years. Either that or they'd be a completely in-character business traveller with a blank corporate loaner phone in accordance with the actual policy of some company they actually worked for. Whatever best matched who they claimed to be.

Their eee-ville devices would stay at home. If they needed ee-ville data, they'd download from the cloud, probably into a new device, after passing the border.