@ofmarconi I think flushing rewrite rules (e.g. via re-saving permalinks) should be part of any site migration procedure. e.g. that’s part of how WP Migrate performs it’s pull / push process. It’s not something that looks controllable from within ASE as it’s not likely able to detect that it’s been part of a newly migrated site. That ‘detection’ should be part of your migration script / process / plugin / etc.
You also mention the need to restart the OLS server, which shouldn’t be necessary as it should be manageable from within WordPress… However, I haven’t worked with OLS much, so, can’t offer any concrete lead / idea / suggestion though…
You can also simply disable custom login URL just before migrating the site and re-enable it on the new destination hosting / server.