LANDLINE phone rings once after I hang up when completing a conversation

[sewwa2]

• My LANDLINE phone rings once after I hang up when completing a conversation.
• It's an AT&T 230 Model
• I've had this phone for years and did not have this problem until I switched to Verizon Fios
• Seems to happen if I've initiated the call to the other number
• I switched to Verizon Fios about 3 months ago
• I also have a home answering machine set up, but it stops working intermittently since I switched to Fios and get the one-ring when I hang up from a conversation
• The desktop answering machine gets all messed up, and I just bought a new one to replace the one I've had

1. What makes the landline ring once after I hang up from a conversation?
2. Why is it messing up my desktop answering machine I have connected to the phone?
3. This is an AT&T Model 230 desktop/wall phone. It is NOT a cell phone