I am currently playing rooms and noticed that the trophies do not pop up when requirements are met so I decided to experiment with different way to get it working and I believe I have found a way.
if you are going after the puzzle pieces trophies, find the level or room that will activate this achievement and before starting it... shut down the game and make a back up copy of this file onto online storage (just in case you need to upload it again) then start up the game again and complete that mission , hopefully it will then get you that trophy I’ve tried it twice now and it has allowed me to get the 80 and 130 puzzle piece trophy
for the mansion complete trophies, same as above before entering the mission required to complete the achievement (the last mission in the mansion) ... exit the game, make a back up copy, start the game again, the complete the mission and then go back to the main menu and the trophy should pop up. I’ve tried it on both the 1st and 2nd mansion trophies and it worked. Just keep trying and hopefully it will work for you guys.
btw I live in the UK so I’m playing the EU version of the game
any questions just reply and I’ll get back to you ASAP. One day they will fix it with a decent patch
all the best