I think coinbox.me is broken. thats true, trusting your funds with a third party involves risk. Just do a batch transaction for those who reach a certain threshold, for example, when a batch of user reached 10k satoshi, send them all in one transaction.
This is technically correct, however you really do not need to have very much money on deposit with the off-chain wallet service as you would almost certainly be giving away very little on a daily basis. If you were to deposit even .0001
BTC with the off-chain wallet service then you would likely have enough to fund payouts for months.
The issue is that if you were to wait until users reach 10k satoshi then most users would never reach enough to get a payout. If for example you gave away 100 satoshi up to once per hour per user then each user would need to visit your faucet 100 times before they would have enough to get a payout, and the amount being paid out would be worth less then a penny and would cost more to spend in additional TX fees then it is worth now