Hi,
Ive had this problem using loo roll tubes, trick is not to over water them. You have said that yours are sitting in water. I still use loo roll tubes but now water using an old fairy liquid bottle (old type) and just squeeze enough water into the top to dampen the potting compost. This has worked for me, no more mould yet (fingers crossed). The cauliflower seeds that ive set in loo roll tubes, pre fairy liquid bottle, were watered with a watering can and have mould on them but the plants are ok.