No, Apple Pay does not disclose your email at all, but if the alias email you used for the merchant is an iCloud alias, then of course any email sent to it would arrive at your iCloud inbox.
iCloud Aliases are not separate email accounts, they are tied to your iCloud account and emails sent to them will arrive to your iCloud email inbox.
The merchant does not know your iCloud address and you can erase the alias at any time to stop receving email to that address.
click here ➜ Add and manage email aliases for iCloud Mail on iCloud.com - Apple Support
If you used some other type of Alias, you would need to explain exactly what you did.