If it varies in its response to test-calls like that, then something odd is going on.
I have no idea whether you have a problem with your phone, or with your phone line.
But, given that your own voice responds, you are getting in touch with your voicemail system in some fashion.
Is it your AT&T voicemail, or the voicemail on your KX phone? I am not sure at this point... but your KX phone seems to be taking no voicemail messages.
So I advise you, at this point, to contact AT&T. Ask them to check your line status, esp. for incoming calls. See if there is any problem ... they appreciate a customer asking for a line check and status check, it helps them find and cure problems with the AT&T network, all the faster.
Let me know how it goes, please. Thanks.