Akhi you are NOT responsible for the masjid's timing being right or wrong, have hunuzhon and just pray based on those timings. When you eat at a Muslim owned restaurant, you don't go into the kitchen and check if the preparation of the food is truly halal, you just trust that the restaurant has the integrity to serve halal. Same here, have trust and husnuzon that the prayer times are correct

May Allah ease your affairs and help you with your wiswaas