Do brown tips prove that indoor air is too dry?
No. Tip damage can have several explanations. Check root-zone moisture, drainage, and recent care changes before attributing it to humidity.
Should I give extra water for brown tips?
Only if the mix is dry at the appropriate depth for that plant. Repeated small amounts of water can leave parts of a pot dry while other areas stay wet.
Can fertiliser be relevant to brown leaf tips?
It can be one possible factor. Note recent fertiliser use and follow the product label; do not add more fertiliser as a response to damaged tips.