IMO, you have two analog lines somehow crossed.
Check that you didn't accidentally press the conference button on one of your phones.
If you are driving existing home or office wiring with the adapter, the previous service may not have been completely disconnected. Do a test with one phone, connected directly to the adapter with a short cord.
Otherwise, the trouble is likely related to the second line on the adapter. Some two- and four-line phones are incompatible with some VoIP adapters. Test with a single-line phone.
If neither of the above apply, try another cord, preferably one with only two conductors (contacts on pins 3 and 4 only).
Though unlikely, this could be caused by a faulty adapter. If your service uses only one line, try configuring it to use line 2 instead of line 1.