If you input that specific alias on the website fancy.com, you will receive it in your main email.
You can only reply to that email as shown by this part above
From: http://mmonium.purity671+store=fancy.com@addy.to
To: mmonium.purity671@addy.to
There is no possible mistake and it’s the default behavior.
It being addy.to or mycustomdomain.com, doesn’t really matter a lot.
Meanwhile, you don’t really have anonymity in that case because the domain will be tied to you, most registrars do quite their fare share of KYC.
If you properly create the email from your service (Addy or SimpleLogin), there is no possible error then.
It doesn’t really matter IMO because you do not need to do that yourself, it’s handled for you.
That’s kinda the point of having a 3rd party alias service yes. 
I’m not sure to understand if you want anonymity or just an email server at this point because if you host your own server + have your own name, then there is literally no anonymity. 
Both Addy and SimpleLogin handle custom domains very well out of the box.
When you’ll receive an email from fancy.com, it will do:
- leaving fancy.com domain servers
- reach Addy’s alias email address
- Addy forwards it to you with the proper interpolation (what you call “encoding”)
- you receive it in your mail client with the proper ready-to-reply safe target
- this is the default behavior of any aliasing service with no additional config needed
The only exception is as I wrote above: when you do need to initialize the email at first, then you need to add it to an alias of your custom domain inside of Addy’s UI.
That’s indeed a feature available in a lot of places, meanwhile this has nothing to do with aliasing and does not add anonymity in any way.
You don’t even need to use any kind of specific service or email server for that, a registrar like Porkbun can do such a thing out of the box.
It is also something available directly from Addy or SimpleLogin if setting up a custom domain.
It will probably also auto-populate the From field properly for you, no need to lock yourself into using a particular email client for such use-case.
I’d like to still emphasize that this has pretty much nothing to do with an aliasing in the sense of anonymity aspect.
Just a wildcard domain catch-all and hence comfort/use of use.
At this point, I am not sure what you’re gaining aside from just giving the company a
simple and hello@mycustomdomain.com, then proceeding with email spam/blocking it or unsubscribing from their stuff.
Sure you could have those being valid:
ola@mycustomdomain.com
bonjour@mycustomdomain.com
asdaskllkjasdljlasd@mycustomdomain.com
working totally fine and hence switch them off independently, but even if you block an ola@mycustomdomain.com, I can just still spam you on ola-again@mycustomdomain.com because the catch-all will just create the address on the fly and forward it towards your main email box.
All of the above emails will still be very much linked to you from A to Z with all the tracking associated with knowing to whom the email goes. 
I’m hence quite concerned about all of this being a huge misunderstanding on what we’re trying to achieve here.
Last point I just read again but
my mailbox looking messy due to the encoded addresses
This shouldn’t be a problem in itself. You’re usually seeing your contacts name or the subject of the email. Or do you actually look at billing@netflix.com every time you do receive an email?
In which case, yes it will look more messy because you’ll have Addy/SimpleLogin being in front of it with the alias but that’s kinda the price to pay while dealing with a 3rd party that serves as anonymity intermediary. 
I mean, if you really want to go hard and it to look slick without adding the email senders as contacts, using folder or other kinds of filtering, I do think there are ways to forward/change the sender’s name on the fly and unwrap all the filters so that even something like this
mmonium.purity671+store=fancy.com@addy.to
could still show up as
store@fancy.com
in your mailbox.
Just as you would have a John Doe being unwrapped into a john@doe.com.
I just haven’t dove too deep on that topic because aesthetics do not matter too much for me. 