If the subdomain and main domain point to the same location (or a subdirectory of the latter), an infinite loop will occur.

In this case you will need to use mod_rewrite (instead of mod_alias) and explicitly check the requested hostname.

But you also used a 301 Permanent redirect. You need to use 302 instead. 301s are persisted by browser caches, so you need to make sure you clear all caches before testing.

Try the following at the top of the subdomain's .htaccess file, before any existing mod_rewrite directives.

RewriteEngine On

RewriteCond %{HTTP_HOST} ^(www\.)?maindomain\.com [NC]
RewriteRule ^mypage\.php$ https://tmp.maindomain.com/rrreee [R,L]

Note that RewriteRule pattern (first argument) matches URL paths that do not start with a slash (unlike the mod_alias Redirect directive).

$0 A backreference contains a URL path that matches the entire RewriteRule pattern. ie. In this case mypage.php. This just saves duplication since you are redirecting to the same URL path at the target.

This defaults to a 302 temporary redirect.