No, the house system wasn't always the same as it is today. Before update 6.4 (November 2001), housing was entirely handled through a manual, key-based system run by players rather than the game itself.
In the very early days, CipSoft introduced rentable apartments but hadn't yet developed an automated system. Administration was handled by community volunteers, most notably lostboy, who effectively acted as Tibia's property manager. He held all the keys, rented out rooms, ran auctions for vacant apartments, and collected rent. Because demand far exceeded supply, apartments were often auctioned to the highest bidder, which became part of the roleplay.
However, the system was messy and fragile. Players frequently failed to pay rent, didn't return keys, or lost them entirely. Since locks couldn't be changed, a missing key meant a room was no longer secure. Some houses became permanently unavailable due to lost or broken keys, and the whole setup was especially vulnerable to map resets, on several occasions, all items stored in rooms were wiped when the map was reset.
Here's a picture, shared by lostboy, showing how house keys were managed in Thais at the time:

This key-based system only lasted a relatively short time. With update 6.4 in November 2001, CipSoft introduced an automated house system, removing keys entirely and replacing them with server-side ownership, access rights, and rent handling. The system we still recognize today.
Sources:
https://www.reddit.com/r/TibiaMMO/comments/1iglwdv/interview_with_lostboy_the_creator_of_fibula/
https://www.nightmareknights.com/historyprojects/flatsystem.html