There are a couple more possibilities: Small animals such as worms, slugs, and millipedes may have created their own channels that now allow the water through. Plant roots may have grown and changed the shape of plastic pots to allow the water through. Whatever the reason, you should look at repotting the plant, even if it remains in the same flowerpot. Filling in the gaps and channels with new potting soil helps replenish the sponge, which will slow the water flow and give more places for roots to grow.
In general, potting soil is porous and allows water to drain away quickly while retaining water like a damp sponge. Depending on where they are in the house, tropical plants and soil may not be drying out; since there is already enough water, the excess is allowed to drain away when you add more. Those plants may need to be watered less than once a week.
On the other hand, succulents and cacti may be in a sandy, fast-draining soil. Depending on where they are in the house, the plants and soil may be drying out quickly, so they may need to be watered more often than once a week.
Before you just pour water into the pot, make sure the plant needs to be watered. It is better to water when the plant needs water than on a weekly schedule.
Try adding water to the saucer instead of the top of the pot. How fast does it soak up? Keep adding water until it no longer gets soaked up. That may show you that you have been adding too much. It also won’t overflow the saucer since you are only adding as much as the saucer can hold. You can try using wider and taller saucers if there is room between plants for bigger saucers. You can also raise the pots up in the saucer so they take up less space. Add some marbles or pebbles to move them up. In all cases of the pot sitting directly in the tray, whether watering from the top or the bottom, do not let the water sit for more than a few hours or else the roots in the bottom of the pot may begin to rot.