What is doing the blocking? Is it the email application or is it the email server?
if it is the server, then the blocks you add should also be applied to the iPad and iPhone. This is how it works for me when I tag a sender as junk. Then all their mail goes to junk and I don’t see it on my iPhone. One setting I use is strict filtering, where all email not in my corporate or personal address books are tagged as junk.
If the application is doing the blocking, usually client side rules, then the blocking will not appear on the iPhone and iPad until the application is opened on the computer. You would have to use the computer, iPhone and iPad apps to tag the sender as junk.