It's very easy to forget to click "Install Mods" when the active mod profile is modified. There may be multiple mitigations:
Rename "Install Mods" to "Apply Mods"?
Make "Install Mods" more prominent in the GUI (i.e. a different color)
When integrating mods, attach a manifest of integrated mods, which can be used to diff against the state of enabled mods in the profile. Any mismatch, such as which mods are enabled/disabled, different versions, should hint the user that they should "Install Mods".
It's very easy to forget to click "Install Mods" when the active mod profile is modified. There may be multiple mitigations: