Answer: Your palms may need some time to become adjusted to their new location but so far it sounds like you are taking great care of them; these plants like average household temperatures, low light, ample moisture in summer and slightly less in the winter when their growth slows, and high humidity which you can provide by misting them or setting the pot in a "pebbles and water tray". The humidity helps to prevent spider mites which thrive in dry air such as most homes experience during the winter season. You should also (gently) vaccuum the foliage regularly or dust it regularly with a cloth dampened in plain water or rinse it with tepid water if the plant is small enough to move -- a sink sprayer or shower will do.
Majesty Palms are called 'self-cleaning palms' because the older fronds fall off the trunk when they die. The yellowing you saw might actually be normal (either due to adjustment or to growth) but the webs would probably have been spider mites. Make sure to check for them periodically as they may reoccur. Maintaining high humidity will help to control them as well.
Millipedes may climb up into the pots while they are being grown outdoors at the producing nursery because they like that constantly moist soil. They will feed on decaying organic matter and possibly on the plants roots. You will need to optimize your watering procedures to try to make it less inviting to them. When you apply water, make it a thorough application (so water runs out the bottom of the pot), and then wait until the surface of the soil dries slightly before watering again. Since you have already tried the drench method, you might also try using diatomaceous earth according to the label instructions to control them. ( I would suggest caution in drenching the soil too frequently as it could result in overwatering the plant.)
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