Despite the very nice post https://webapps.stackexchange.com/a/25531/24693 it seems that I still don't understand Gmail's "Treat as an alias" option (the main thing I took away from that post was that if an address is technically "me" or mine, the intention is that i mark it as an alias, whereas if it's my boss or something, I would not check the option).
My problem: If I do not have this option checked, then when I reply all, it includes my address in the recipients, and I end up with the reply (that i've sent) in my inbox. If, on the other hand, I do mark the address as an alias, then messages I send (not even reply alls) are always in my inbox.
UPDATE: Even when the address is not an alias, sent mail from the address goes to my inbox
I would like to send mail and have those messages not in my inbox.
Best Answer
So I found https://webapps.stackexchange.com/a/42968/24693 which I think solves my problem. I had a filter
I changed it to:
n.b. despite me entering the new rule as above, it appears as follows in my filters list