There is more than one Plain old telephone service interface/protocol (it's the protocol your phone is speaking to ATA device and is used for transfer of basic events like "do ringing", "earphone picked up" and so on). Althougth the protocol is very simple (it can be mostly expressed in the terms of voltage and resistance), both devices needs to speak compatible way.
It's even worse, some phones may be more tolerant for unexpected deviations in parameters than other.
See Voice->Regional->Miscelaneous section and Voice->Line n->FXS Port Polarity Configuration
You need to configure values according your phone device requirements. It may not be esay to found the phone specification, but all you needs is "what country the phone has been manufactured for" In most cases there is single specification of parameters of POTS line per country so follow it.
If your two phones have incompatible requirements then reconfigure one or both of phones first if possible. If not possible, then you can't connect both devices to one ATA at the same time.
