You need to read a bit more about two or more MX
records.
The priority shows what order of priority of the inbound mail servers that you, as a domain owner, want the senders to be trying to deliver the message to, with lowest number being highest (e.g. first) priority.
When you’re having multiple MX
records like this, …
Senders (that are following the standards) will try the first MX
(lowest number, highest priority), which in your example is “mail.example.com
”, and if that delivery is successful, everything is good, and the sender WILL NEVER try to deliver that specific message again.
If the delivery to “mail.example.com
” is unsuccessful, such as e.g. due to connection interruptions, the sender will re-try the next one in order of the priority (0, 1, 2, 3, …), until a delivery can successfully be made.
So when the delivery towards the server “mail.example.com
” failed, the sender will re-try on “example-com0i.mail.protection.outlook.com
”, according to your example.
The first mail server, in the order of the priority (and successful delivery), is the one that is winning the delivery for that specific message, when you have multiple MX
records.
If you require two or more different mail servers (e.g. “mail.example.com
” and “example-com0i.mail.protection.outlook.com
”) to be synchronized, then you will need to handle the synchronization between them on your own.

That awesome advice by @cscharff could for example be one way, to handle the synchronization between multiple servers, if that is required for your set up.
Such kind of “internal” forwarding can also be used, if you require “user1” and “user2” to be on separate storage servers.
But all these things are something you need to handle after the message has been delivered to either of the MX
records.
Multiple MX
records allows senders to “failover” to another mail server, and (hopefully) still be able to deliver the message, if one (or more) mail servers are unreachable.
Multiple MX
records will NOT make the senders deliver the message to all 2, 3, 4, …, 10 (or how many different) MX
records that you have set up.
One single message will only be delivered one time, and NOT once per MX
record.